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Properties of Logarithm
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0203.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0204.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. b0 =3D 1
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0205.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0206.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0207.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0201.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0198.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0199.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0200.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
<= /div>
4. log(x) =3D t·logb(x)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0177.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
<= /div>
4. log(x) =3D t·logb(x)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
We veryif= y part 2: logb(xy) =3D = logb(x) + logb(y),  x, y > 0.
Proof:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0178.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
<= /div>
4. log(x) =3D t·logb(x)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
We veryif= y part 2: logb(xy) =3D = logb(x) + logb(y),  x, y > 0.
Proof:= 3;
Let x and= y be two positive numbers.
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0179.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
<= /div>
4. log(x) =3D t·logb(x)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
We veryif= y part 2: logb(xy) =3D = logb(x) + logb(y),  x, y > 0.
Proof:= 3;
Let x and= y be two positive numbers. Let log(x) =3D r=
and logb(y) =3D t, which in exp-form are x =3D b<= /span>r and y =3D bt.
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0180.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
<= /div>
4. log(x) =3D t·logb(x)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
We veryif= y part 2: logb(xy) =3D = logb(x) + logb(y),  x, y > 0.
Proof:= 3;
Let x and= y be two positive numbers. Let log(x) =3D r=
and logb(y) =3D t, which in exp-form are x =3D b<= /span>r and y =3D bt.       
Therefore x·y =3D br+t, =
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0181.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
<= /div>
4. log(x) =3D t·logb(x)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
We veryif= y part 2: logb(xy) =3D = logb(x) + logb(y),  x, y > 0.
Proof:= 3;
Let x and= y be two positive numbers. Let log(x) =3D r=
and logb(y) =3D t, which in exp-form are x =3D b<= /span>r and y =3D bt.       
Therefore x·y =3D br+t, which in log-form is
logb(x·y) =3D r + t =3D logb(x)+logb(y).
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0182.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
1. logb(1) =3D 0
2. log(x·y) =3D logb(x)+logb(y)
<= /div>
3. log(    ) =3D logb(x) – logb(y)
<= /div>
4. log(x) =3D t·logb(x)
x<= /div>
y<= /div>
1. b0 =3D 1
2. br · b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t =3D br+t
3.      =3D br-t
4. (br)t =3D brt
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>t&#= 13;
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>r&#= 13;
Properties of Logarithm
Recall the following
Rules of Exponents:
The corre= sponding
Rules of = Logs are:
We veryif= y part 2: logb(xy) =3D = logb(x) + logb(y),  x, y > 0.
Proof:= 3;
Let x and= y be two positive numbers. Let log(x) =3D r=
and logb(y) =3D t, which in exp-form are x =3D b<= /span>r and y =3D bt.       
Therefore x·y =3D br+t, which in log-form is
logb(x·y) =3D r + t =3D logb(x)+logb(y).
The other= rules may be verified similarly.
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Example A:
3x2
Öy
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
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3x2
Öy
log(      ) =3D log= (      ),
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
Example A:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0184.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
Example A:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0185.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
     product rule           = ;            &n= bsp;   
        = ;      =3D log(3) + log(x)
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
Example A:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0186.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
     product rule           = ;            &n= bsp; power rule 
        = ;      =3D log(3) + log(x2) – ½ log(y)
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
Example A:
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3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
     product rule           = ;            &n= bsp; power rule 
        = ;      =3D log(3) + log(x2) – ½ log(y)   
        = ;      =3D log(3) + 2log(x) – ½ log(y) <= /span>
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
Example A:
------=_NextPart_01C8F646.8A17FA70 Content-Location: file:///C:/89565D6D/2PropertiesofLogarithm_files/slide0188.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
     product rule           = ;            &n= bsp; power rule 
        = ;      =3D log(3) + log(x2) – ½ log(y)   
        = ;      =3D log(3) + 2log(x) – ½ log(y)
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
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3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
     product rule           = ;            &n= bsp; power rule 
        = ;      =3D log(3) + log(x2) – ½ log(y)   
        = ;      =3D log(3) + 2log(x) – ½ log(y)
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
log(3) += 2log(x) – ½ log(y)     power rule =
=3D log(= 3) + log(x2) – log(y)    
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
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3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
     product rule           = ;            &n= bsp; power rule 
        = ;      =3D log(3) + log(x2) – ½ log(y)   
        = ;      =3D log(3) + 2log(x) – ½ log(y)
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
log(3) + 2log(x) – ½ log(y)     power rule =
=3D log(3) + log(x2) – log(y)     product rule= 3;
 
=3D log (3x2) – log(y)   
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
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3x2
Öy
log(      ) =3D log= (      ), by the quotient rule
        = ;      =3D log (3x) – log(y)
     product rule           = ;            &n= bsp; power rule 
        = ;      =3D log(3) + log(x2) – ½ log(y)   
        = ;      =3D log(3) + 2log(x) – ½ log(y)
3x2
Öy
3x2
 y1/2
Properties of Logarithm
a. Write log(      ) in terms of log(x) and log(y).
log(3) + 2log(x) – ½ log(y)     power rule =
=3D log(= 3) + log(x2) – log(y)     product rule= 3;
 
=3D log = (3x2) – log(y1/2)=3D log(      )     &nb= sp;
3x2
 y1/2
b. Combine log(3) + 2log(x) – ½ log(y) into one log.
Example A:
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Recall that given a pa= ir of inverse functions, f and f ,
then f(f -1(x)) =3D x and f -1(f(x)) =3D x.=  
Properties of Logarithm
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Recall that given a pa= ir of inverse functions, f and f ,
then f(f -1(x)) =3D x and f -1(f(x)) =3D x.=  
Since expb(x) and logb(x) is a pair of inverse functions,
Properties of Logarithm
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Recall that given a pa= ir of inverse functions, f and f ,
then f(f -1(x)) =3D x and f -1(f(x)) =3D x.=  
Since expb(x) and logb(x) is a pair of inverse functions,
we have that: 
a. = logb(expb(x)) =3D x or log(b= x) =3D x
Properties of Logarithm
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Recall that given a pa= ir of inverse functions, f and f ,
then f(f -1(x)) =3D x and f -1(f(x)) =3D x.=  
Since expb(x) and logb(x) is a pair of inverse functions,
we have that: 
a. = logb(expb(x)) =3D x or log(b= x) =3D x
b. expb(logb(x)) =3D x or blog (x)=  =3D x     
Properties of Logarithm
b
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Recall that given a pa= ir of inverse functions, f and f ,
then f(f -1(x)) =3D x and f -1(f(x)) =3D x.=  
Since expb(x) and logb(x) is a pair of inverse functions,
we have that: 
a. = logb(expb(x)) =3D x or log(b= x) =3D x
b. expb(logb(x)) =3D x or blog (x)=  =3D x     
Properties of Logarithm
b
Example = B: Simplify
a.  log2(2-5) =3D
b. 8log  (xy) =3D
c. e2+=3D
8
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Recall that given a pa= ir of inverse functions, f and f ,
then f(f -1(x)) =3D x and f -1(f(x)) =3D x.=  
Since expb(x) and logb(x) is a pair of inverse functions,
we have that: 
a. = logb(expb(x)) =3D x or log(b= x) =3D x
b. expb(logb(x)) =3D x or blog (x)=  =3D x     
Properties of Logarithm
b
Example = B: Simplify
a.  log2(2-5) =3D -5
b. 8log  (xy) =3D
c. e2+=3D
8
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Recall that given a pa= ir of inverse functions, f and f ,
then f(f -1(x)) =3D x and f -1(f(x)) =3D x.=  
Since expb(x) and logb(x) is a pair of inverse functions,
we have that: 
a. = logb(expb(x)) =3D x or log(b= x) =3D x
b. expb(logb(x)) =3D x or blog (x)=  =3D x     
Properties of Logarithm
b
Example = B: Simplify
a.  log2(2-5) =3D -5
b. 8log  (xy) =3D xy
c. e2+=3D
8
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