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Calculation with Log and Exp
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0003.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
Example: Find the answer to 3 significant digits
 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
Example: Find = the answer to 3 significant digits
&= #13;
a.103.32        = ;             b. Öe <= /span>
  
&= #13;
c. log(4.35)        = ;       d. ln(2/3)
  
 
6
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0004_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAACZmQIEjI95BQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
Example: Find = the answer to 3 significant digits
&= #13;
a.103.32        = ;             b. Öe 
   »2090
a.
c. log(4.35)        = ;       d. ln(2/3)
  
6
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0005_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAACZmQIEjI95BQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0005_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhnQBKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQCb AEcAgAAAAACZmQL/hI+py+0YAouv2ouz3nxKRXXiSJamB4bnyrauEX2w+tb2XcUQjff+rdL9hsRW SAgpKpeYI4/HjEphAORsis1aq7Ksd/mEfse4rZiMdpm76bYxLImx3XQOVI6v61f57f6/gecHqCVn IkhIJjiY2JiyyOjoaPgoabkzd3B2+RfJxWnpuQlaN+pJ2jaYh5oIichaRBlIAQk7VGs3aguE23G6 a7NK8gt8K3tBXPzimpupXLY4kgzy7DvtcGxxXR1MLMw99T0TDe7l2lv+de6c3u7+Dh8vP08flV1f otu0jd+gn8GvX4J/yQKi+VdD3zWDYxgOYzdOg8NCCB9AXHCqIqZLrfdyAbwYcKIUWhpR7LN4EVvK VCQhZlypyWXJHZKCsCMIk4tMaTkb2szkLaepVx8nsRGDsOLQcT0/NUoKE+pNGhpFKoF6UptMGQtn QhMnsWfUrRH3Ne3BzJoaXeS0nv3K1euVN26byu025+5df2+RCW3L4o7evnwJqxQLmM9RhnsxGi48 6zHKtNYkD1zrhjJPywk5D7RqtRI3sJu7PSOdz49nYKhPaBZ42UfidwUAADs= ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0005_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwASAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAC AA4AgAAAAACZmQIEjI+pWwA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0005_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhcgA3AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBv ADQAgAAAAACZmQL0hI+pGOsPo5y0wtCs3rxrnHniSFpYiabUOYHqCyesNMe2Gl71zffG7gtycgug sEX8pUDGA8vFawKIO+mHmWRgoRUmTZrj/rJDq3NrPnsj2OKsCiTL5N/2SvxwGblwd29LQvaUxVd4 pIB31QS19+Zlh5IWmKg1Rug41QBZQolDZ9mZqXayOXnIxoc4FxJ6eiTpGis7S1tre4ubq7vL2+v7 CxwsPExcbHyMnKy8zNz8+uQc1RrNOU395aBpfY1YOsXdgfYJfodJPsK47Sx+iXbu5t7t/Z53SQ/f 6HfPbkeprsxvVTZ29+DpWFNQX0IRsBZecBihAAA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
Example: Find = the answer to 3 significant digits
&= #13;
a.103.32        = ;             b. Öe =3D e= 1/6
   »2090
&= #13;
c. log(4.35)        = ;       d. ln(2/3)
  
6
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0006_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAACZmQIEjI95BQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
Example: Find = the answer to 3 significant digits
&= #13;
a.103.32        = ;             b. Öe =3D e= 1/6
   »2090        = ;            &n= bsp;    » 1.18
a.
c. log(4.35)        = ;       d. ln(2/3)
  
 
6
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0007_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAACZmQIEjI95BQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0007_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAB AAIAgAAAAACZmQICTAoAOw== ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
Example: Find = the answer to 3 significant digits
&= #13;
a.103.32        = ;             b. Öe =3D e= 1/6
   »2090        = ;            &n= bsp;    » 1.18
a.
c. log(4.35)        = ;       d. ln(2/3)
   »0.638
6
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0008_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAACZmQIEjI95BQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0011.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Need a calculator for this section.
All the problems are in base 10 or base e. 
Example: Find = the answer to 3 significant digits
&= #13;
a.103.32        = ;             b. Öe =3D e= 1/6
   »2090        = ;            &n= bsp;    » 1.18
a.
c. log(4.35)        = ;       d. ln(2/3)
   »0.638        = ;            &n= bsp;   » -0.405
 
6
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0011_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAACZmQIEjI95BQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0011_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUwAqAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgBQ ACgAgAAAAACZmQKhTICpy+0PozRG2oszo1z7f1FIxXXgmZUlUCWqiqIvPIrOjB9fzt92yAsKX6lf jDWkHWutpTNmekp3xqnVEr1qIdmtd9H9isNiL7msPaOt6rW07XbC48c5XVa9P1d69iHfB/XXFLhE QlgoiKSTWDfI2Ii3GOlYQ6mIdCmZqQnS0tPJpdMU1Jc0CrkxhHXaaoIY4SpLpAHriUNnG1q0K9N7 UgAAOw== ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
The same problems may be stat= ed in different form= s:   <= /span>
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Find = the x to 3 significant digits
&= #13;
a. log(x) =3D 3.32      &= nbsp; b. 1/6 =3D ln(x)
        
&= #13;
 
c. 10x = =3D 4.35        = ;      d. 2/3 =3D ex&= #13;
        
The same problems may be stat= ed in different form= s:   <= /span>
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0013_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AAMAgAAAAACZmQIDRG4FADs= ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Find = the x to 3 significant digits
&= #13;
a. log(x) =3D 3.32         b. 1/6 =3D ln(x)
         x =3D103.32
         x » 2090
 
c. 10x = =3D 4.35        = ;      d. 2/3 =3D ex&= #13;
        
The same problems may be stat= ed in different form= s:   <= /span>
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Find = the x to 3 significant digits
&= #13;
a. log(x) =3D 3.32         b. 1/6 =3D ln(x)
         x =3D103.32        = ;           e1/6 =3D x
         x » 2090        = ;           1.18 » x =
 
c. 10x = =3D 4.35        = ;      d. 2/3 =3D ex&= #13;
       
The same problems may be stat= ed in different form= s:   <= /span>
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0015_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhmgKVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCX ApAAgAAAAPAoRQL/hI+py+0Po5y02ouz3rz7D4aiGATjiabqyrbuC8fyTNdzWdr6zvf+DwwKh0QQ LldMKpfMpvMJjWqOJqn1is1qt1wutdoNi8fksvn8yOHQ7Lb7DY+/1mu5/Y7P69108P4PGCg4yNPn t3FEqLjI2IjX10HlOElZaYmlhoTxdXjp+QkaKpOZgETH8CWqusraypF6wJm4oOlqe4uLKxkrW5v7 Cxy8ugvQWyeMnKzMOGtgSLwcLT0Nd1ysmUhKvc3dLVU1S/zc6V1ufr5jXBduje7+Dr+SrQ7WHn+P n7+JzX/crA8woMBI/wYaPIiQFrSEDBsGhOUwokR4mchNvIhxmaGM/xw7JoPkMaTIW9pGmjz5aSHK lSwVFWwJM6YeXzJr2ryJM6fOnTx7+vwJNKjQoUSLGj2KNKnSpUybFrLoNKpUhVCnWo1qz0bVq1z1 ZdW6tatYd19rlB2L9tzZCmsj0EwL11xbCnPThI2LV1ndCS/Z3s0LGNhevm8l9B0cOHElxAiqFibs r6/iySn/KnTw+FqDhSope8bE6QRjZ2pQQX0JkfToz6yD0DOS2e61Tl9rm2gnubVuJuQ677NcqqKC twVpGwe+Ozlv5JtjYwZHk3j04YdWK78uxLlb7c1VB+/tK3q93NjLLyfInJfq6hbFU1dv3bx8s+m/ T4FeK6s97prn+/9XEt9siODnR2H71fdfgq4hyAuDkPRjmnEKEqKOUvxFOCBp/ZV1oBYXBkgZPakJ FR+Iwo1o3xiDgRiYLM2xaNKFVL3CTlsyLscfecr51l1OKn1Y4I1UsffIXjDGtZqQGBnTIF3jMRic IDqm6J+SGsrE2XhOPjmJkFM2ZiVgYR5p0GP8bOldl8x92eR/UIbpkGNaQiYgJTeymWaV90EZkilA 3gYnHzLieWUsE9L5E4SGCWfnoCvmp5+fCZKZkaLbFRcIe8g9qml4Z0bG51SULhmkZbDwWM1rUYIJ XHH/WCNiqE2NehGs3KUS2kyvjdOgqa+K46mqIQYqknhrVeihc6b/UOfieqeymRqjda43W5CeEdqS geT1AoN1qKHYq62Q4qfhOH9VROA64la7qmLYssRhbLnO8e68yLL6q63qVRvan/2oWyqgvU327kpn HVswjYD6Ja24weYL6b7cOrvdtALnOe2OxPaZGcIbX+Bne50W2l+439XYDMD8ZlwyBJJSi3Ex5dFa a8fKfmyBypexmma+Lbs4jzN1qvsB0THPFzKJ8sqqwpk/a5qnzwCbW27PTLeLc2LS8kTuc1ej4HRk PLMLs9W5Qkwy2HMe6uzXE21tGoCfNms2vm2u/N7YLYvmNNvg+vhl1nyTy+SVuIG6p6Hy9H0oqjdB 6/YIRE+d9IHW/z5h6YSO24QnzbCla3fbZmQ+acIouYdhEugSafLoSfstdk/j2hV5CPPuW3YZOmt+ L+B4ey23gSejsRHsf+N0PLOqmzn8GckjLXhHjEX/+Za1A2E620x5Pkr22n8fA/fhew9++S2ITy/6 5q+fgfrnk89+/LZT3z398t+f8/Xj249//xUnyz//CTBuANTfAA/YLtAEEIEIXOD7HMhAAUJwcROM 4P3c9z4LanB+BuxWBzfYPwyCcIRLqCAJT5gdE6JwhT0QIQtfqAMXwnCGN1AhDW/IAhnicIcpgB8P fwiWDwJxiJKzIRGP2D4jInGJiGKiExckxCdKcVFRpEasrojFKd8GQ4eZwqIXvwhGMGpxGLoIoxnP iEYxjnFYaVTjGoHYxsK9UYtx5OIc/VfHO+qxbWbcox7z6Mc31rGKgZTfIH1YyAseUkSJHOAiH9nI ED5ykJGU4CQ3V0kQXjKTPLwkITlZJU9+EpRumiQpiQDIpZzxlFYQJSaz9UVWbqF3e5JjC13pxTDE UpZdmFgObdk0XApzlFS8Ii/BFsRXUvB2tcxiDNGYPmce0wUipBsUackvaV5hlZfi5jSfqT9r4qiN cRgmIr+ptquJs4DKzIM30fmNggETnj9MJT2duMt7DrEAADs= ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Find = the x to 3 significant digits
&= #13;
a. log(x) =3D 3.32         b. 1/6 =3D ln(x)
         x =3D103.32        = ;           e1/6 =3D x
         x » 2090        = ;           1.18 » x =
 
c. 10x = =3D 4.35        = ;      d. 2/3 =3D ex&= #13;
        x=3Dlog(4.35)
        x » 0.638
The same problems may be stat= ed in different form= s:   <= /span>
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0017.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Find = the x to 3 significant digits
&= #13;
a. log(x) =3D 3.32      &= nbsp; b. 1/6 =3D ln(x)
         x =3D103.32        = ;           e1/6 =3D x
         x » 2090        = ;           1.18 » x =
 
c. 10x = =3D 4.35        = ;      d. 2/3 =3D ex&= #13;
        x=3Dlog(4.35)        ln(2/3)=3Dx
        x » 0.638        = ;    -0.405 » x =
 
The same problems may be stat= ed in different form= s:   <= /span>
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
    
Example: Solve 25 =3D 7*10
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0020.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
To solve exponential equations:
• isolate the exponenti= al part
    
Example: Solve 25 =3D 7*10
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
To solve exponential equations:
• isolate the exponenti= al part
    
Example: Solve 25 =3D 7*10x= 3;
Isolate the exp-part:     25/7 =3D 102x  
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0024_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOAAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALCIACwAJ ABAAgAAAAP//AAIXhB8IyavW4plTNkgtxVhzJW2VEzrjVgAAOw== ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 25 =3D 7*102x
Isolate the exp-part:      25/7 =3D = 102x
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0021_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZwE4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUAAQBR ATUAgAAAAP//AAL/hI+py+0Po5wzAIuvznz7Dn5iSI5mSKXqyrbuC8fyTNf2jef6Dpf+CfwJg8Sh sYg8WnjMplOx1Bii1EN1as1it9Lu1asFc7/kcHlsTqPX4vb5CY9Dk3Rl/W7P4/f6vkkOGBOFMBhG uFDIdTjHmJDYteiIONkYaWmIqZgJufnoSSkZuONHymdainqqmsq6ygn4FqvmNivLZkt7W7ur25v7 ixvMCzwszNbUmuyqzLzs3Az9DCRKXW19jZ39Es0t3f3tHQ4+ThdpTOx7rl7Mnt6ODr/uPh//Ll+v S64vzr/v3w+wVaVOoC5pOvgq4aeBCBeGemgwobYHDiNWJMhQYUGM9xDT/PvobKLICCBL4jt5L+Ww kSydqKT3kpbJbi1r2swyc8/NnTx7+twWsNzPoURd5ESBclPRpUzjxFyXoanUqUz3Ub2KderFhhuz ev0qtRTYsWSz4iqLNm1YD2rbun0LN67cuRJi0r2LFwK5vHz5btWY8VHfwV6PsiWMeOlTe+8SOxZp 2M/jyZQrW84WOeTlzTQWw2RMj7PoCkENjz5NsSvgjlwDq/6LOjbO0rSHyL6d9LPu3L9wj84sOLVk 38SLGwf7DxmS46I9t4G1kjnlaCORSt/8F/b17U5Ncf+O7Rz48daOkD+PPj32w+rbh3cPH7PE+PRp FAAAOw== ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 25 =3D 7*10
Isolate the exp-part:     25/7 =3D 102x (=3Dexp<= span lang=3DEN-US style=3D'font-family:Verdana;font-size:89%;text-shadow:auto; color:#F02845;position:relative;top:.37em;mso-text-raise:-25%;mso-fareast-= language: ZH-CN'>10(2x))
        = ;            &n= bsp;            
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0037.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 25 =3D 7*10Isolate the exp-part:     25/7 =3D 102x (=3Dexp<= span lang=3DEN-US style=3D'font-family:Verdana;font-size:89%;text-shadow:auto; color:#F02845;position:relative;top:.37em;mso-text-raise:-25%;mso-fareast-= language: ZH-CN'>10(2x))
   log(25/7)= =3D 2x      <= /span>
        = ;            &n= bsp;            
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 25 =3D 7*10
Isolate the exp-part:     25/7 =3D 102x (=3Dexp<= span lang=3DEN-US style=3D'font-family:Verdana;font-size:89%;text-shadow:auto; color:#F02845;position:relative;top:.37em;mso-text-raise:-25%;mso-fareast-= language: ZH-CN'>10(2x))
   log(25/7)= =3D 2x      <= /span>
        = ;            &n= bsp;             log(25/7)        
2
=3D x 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0026_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhTwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQBL AAEAgAAAAACZmQIHjI+py+3fCgA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Exponential equations are equations with
the unknown in the exponents.
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 25 =3D 7*10
Isolate the exp-part:     25/7 =3D 102x (=3Dexp(2x))
   log(25/7) =3D 2x     
        = ;            &n= bsp;             log(25/7)<= span lang=3DEN-US style=3D'font-family:Verdana;font-size:133%;text-shadow:auto; color:#009999;mso-color-index:6;mso-fareast-language:ZH-CN'>        
2
=3D x <= span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;fon= t-size: 133%;text-shadow:auto;color:#009999;mso-color-index:6;mso-fareast-language: ZH-CN;mso-char-type:symbol'>» 0.276
 
Exact answer
Approx. answer
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0027_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhTwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQBL AAEAgAAAAACZmQIHjI+py+3fCgA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0027_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGwAPAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABQAW AAoAgAAAAACZmQIbhI8Jwa1/GoNUUuXcNTOGrW1IJ3pf6aHJqSIFADs= ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0027_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAQAb AA4AgAAAAACZmQIlhI+pGLH/moPUyFovhnqv7iVgeIzYZDVkmqKrpK6lScKxbN9rAQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0027_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhxgA4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADE ADYAgAAAAAAAAAL/DI6py+0PIzCy2ouzPnT7X3XgSJahiY5iyrbe6sYOLNd2Qt91rvcs7/sFhy4g sWQ8Ki3J5csJ3TSjmCkxgM1qt9yu9wvWUlPWYdmHHaPOaDWO7W7AdXNbOq7Cc/R3/ZPPV+c34Sco 0zeYYXgYmChV2OioCImHKHkCWLlYSRlneRmxWRQJismpWcrU6faZKreq1uq6INpSS3Y7lrtGOjsD q7sbJYzU68tATJIMInu8l+m5rCT9QS1lbQZM1eyMreFdBd4jfkEeYm6nPYy+ow7FfcweauyM4+4E 7ysPsT/Tb1sojMCBBL3Ue3UwW0IF/1w1JLMwyENeEcdVRDARVMZiKBdvbFTW0WPIj45IMguZrqPJ QSv/oIzR8tFLmCNnwiyIM6fOgTZjFAAAOw== ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      = 3;
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0030.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      = 3;
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0031.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 8.4
        = ;            &n= bsp;            = ;             = 3;
 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 8.4
        = ;            &n= bsp;            = ;             e2-3x =3D 8.4/2.3
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 8.4
        = ;            &n= bsp;   (expe(2–3x)=3D= ) e2-3x =3D 8.4/2.3 = ;
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 8.4
        = ;            &n= bsp;   (expe(2–3x)=3D= ) e2-3x =3D 8.4/2.3 = ;
        = ;     2 – 3x =3D ln
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0036_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlheABAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALFAAAAAi AD4AgAAAAAD//wKmhI8Wt8qf3JqA2oovjbx7pGViSDaYg56qyUrjS8KRCXI05MY63Kb9imvshrKP 8Sgj6n7MoDMJJSZuyA+1is1qt9yu9wsOi8fk2lVMveSir3JHyd40fU/VAy6d2fb6e/wPRCcYaPaX 5zZlCDhHyOiHB8WX2DeJaHmJmam5yVmm9oZTM3gGGdJZWGpHyeiIqrhhJSl6lPopyVqXWKvauQt7 W9eqtZNQAAA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 8.4
        = ;            &n= bsp;            = ;             e2-3x =3D 8.4/2.3
        = ;     2 – 3x =3D ln(8.4/2.3)
        = ;            &n= bsp;    2 – ln(8.4/2.3) =3D 3x       
 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 8.4
        = ;            &n= bsp;            = ;             e2-3x =3D 8.4/2.3
        = ;     2 – 3x =3D ln(8.4/2.3)
        = ;            &n= bsp;    2 – ln(8.4/2.3) =3D 3x       
        = ;            &n= bsp;         2-ln(8.4/2.3)        
3
=3D x 
 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0034_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhbgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBr AAIAgAAAAACZmQINjI+py+0Po5y02otRAQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0034_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAA3AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCL ADYAgAAAAAAAAALDjI+py+0Po5wUgYuz3rz7D4biSJaAYabqyrYr6sbyTINwjee6ee/+D+wBh0SZ sIhMko7KplPDfEqV0al1WL1qddmtd9b9ilnhsblUPqttgbX71X7Ll/G5/ZO+u/N6Nb9v9gcoJjjo VWiohZhotcgo5fjoFClJVVf5RolZpLmJdel51hnqM0rKBXr6Zapaw9oKlgp79TrrUmtLJpv7hMub 4vuLtiucFFwscozMtgxJ3Bz0DF0qPY1qbYltXMHd7f0NDl4AADs= ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
To solve exponential equations:
• isolate the exponenti= al part
• bring down the expone= nts by restating in    
   log-form. =
    
Example: Solve 2.3*e+ 4.1 =3D 12.5
Isolate the exp-part: 2.3*e2-3x + 4.1 =3D 12.5
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 12.5 – 4.1<= /span>        = ;     
        = ;            &n= bsp;            = ;      2.3*e2-3x =3D 8.4
        = ;            &n= bsp;            = ;             e2-3x =3D 8.4/2.3
        = ;     2 – 3x =3D ln(8.4/2.3)
        = ;            &n= bsp;    2 – ln(8.4/2.3) =3D 3x       
        = ;            &n= bsp;         2-ln(8.4/2.3)        
3
=3D x <= span lang=3DEN-US style=3D'font-family:Symbol;mso-ascii-font-family:Verdana;fon= t-size: 133%;text-shadow:auto;color:#009999;mso-color-index:6;mso-fareast-language: ZH-CN;mso-char-type:symbol'>» 0.235
 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0038_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhbgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBr AAIAgAAAAACZmQINjI+py+0Po5y02otRAQA7 ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0038_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAAE4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAD+ ADYAgAAAAAAAAAL/jI+py+0Po5z0gIuz3rz7D4bi+AXkiabqyoJmC8fy+s72jct1zvfq7gsKecCh 0Vg8KpejJPOpg0qnGif12sRql9att/oN97piL7mMJp2nlbY7kY631lL60yDPp+x3NF4PKMLHNKj0 F4jYUWjot5gY5ojU+EiZETl0GXRY+ZipOclJ6ekzSlQaSph2irOJCrjKCuoaCHtTO9M6K3eLK6ub xxtVlvvrp+pbfGw8HJxs0wwDzULs/CU9jVwNqSxGra11TZP9vRX+M06OZb6Hnk61jgKvJu/uwg1J X++RL9iu37esG79/YALiIwjunrWBCC8wLOGvoSSDCyW+U2jmIUKNSooiWvzU6I1ICh/rlMR2MlVK disZtTzB8V9MRDPr1Xz18shNPTvJ9dyVc2LQED+1FcU4NFZSe0vHNIX4NMfRkCOrWr2KlWRUDgUA ADs= ------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Log equations are equations with the <= span lang=3DEN-US style=3D'font-family:Verdana;font-size:156%;text-shadow:auto; mso-fareast-language:ZH-CN'>unknown in the logs.
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0040.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Solve 9*log(2x+1)=3D 70
Log equations are equations with the <= span lang=3DEN-US style=3D'font-family:Verdana;font-size:156%;text-shadow:auto; mso-fareast-language:ZH-CN'>unknown in the logs.
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0041.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Log equations are equations with the <= span lang=3DEN-US style=3D'font-family:Verdana;font-size:156%;text-shadow:auto; mso-fareast-language:ZH-CN'>unknown in the logs.
To solve log equations:
• isolate the log part =
    
Example: Solve 9*log(2x+1)=3D 7
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0043.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Solve 9*log(2x+1)=3D 7
Isolate the log part:   log(2x+1) =3D 7/9 
Log equations are equations with the <= span lang=3DEN-US style=3D'font-family:Verdana;font-size:156%;text-shadow:auto; mso-fareast-language:ZH-CN'>unknown in the logs.
To solve log equations:
• isolate the log part =
    
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0058.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Log equations are equations with the <= span lang=3DEN-US style=3D'font-family:Verdana;font-size:156%;text-shadow:auto; mso-fareast-language:ZH-CN'>unknown in the logs.
To solve log equations:
• isolate the log part =
• drop the log and rest= ate in the exp-form
    
Example: Solve 9*log(2x+1)=3D 7
Isolate the log part:   log(2x+1) =3D 7/9 
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0059.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Solve 9*log(2x+1)=3D 7
Isolate the log part:   log(2x+1) =3D 7/9
Restate in exp-form:  2x + 1 =3D exp10(7/9)
        = ;            &n= bsp;          
Log equations are equations with the <= span lang=3DEN-US style=3D'font-family:Verdana;font-size:156%;text-shadow:auto; mso-fareast-language:ZH-CN'>unknown in the logs.
To solve log equations:
• isolate the log part =
• drop the log and rest= ate in the exp-form
    
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0060.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp
Calculation with Log and Exp
Example: Solve 9*log(2x+1)=3D 7
Isolate the log part:   log(2x+1) =3D 7/9
Restate in exp-form:  2x + 1 =3D exp10(7/9)
        = ;            &n= bsp;           2x + 1 =3D 107/9  &= nbsp;
Log equations are equations with the <= span lang=3DEN-US style=3D'font-family:Verdana;font-size:156%;text-shadow:auto; mso-fareast-language:ZH-CN'>unknown in the logs.
To solve log equations:
• isolate the log part =
• drop the log and rest= ate in the exp-form
    
------=_NextPart_01C82DF7.70F11940 Content-Location: file:///C:/2253A370/6CalculationwithLogandExp_files/slide0061.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Calculation with Log and Exp