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The Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0211.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
The Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0212.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52
The Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0213.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x
The Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0214.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
The Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0215.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25
The Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0216.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
The Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0217.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0218.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
We called this exponent 2 as “the log (logarithm) of 25 in base 5”,
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0219.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
We called this exponent 2 as “the log (logarithm) of 25 in base 5”, and write this relation as 2 =3D log5(25).
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0220.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
We called this exponent 2 as “the log (logarithm) of 25 in base 5”, and write this relation as 2 =3D log5(25).
In genera= l if bx =3D y,
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0221.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
We called this exponent 2 as “the log (logarithm) of 25 in base 5”, and write this relation as 2 =3D log5(25).
In general if b= x =3D y, we called the exponent x as =
“ t= he log of y in base b”
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0222.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
We called this exponent 2 as “the log (logarithm) of 25 in base 5”, and write this relation as 2 =3D log5(25).
In general if b= x =3D y, we called the exponent x as =
“ t= he log of y in base b” and write it as x =3D logb(y).<= /span>
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0223.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
We called this exponent 2 as “the log (logarithm) of 25 in base 5”, and write this relation as 2 =3D log5(25).
In general if b= x =3D y, we called the exponent x as =
“ t= he log of y in base b” and write it as x =3D logb(y).<= /span>
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
In other = words, the output “logb(y)”= ; is= “an exponent x”,
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0224.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The expon= ential function bx is also w= ritten as expb(x).
Example = A: Write the following in exp-notation.
a. 52           = ;exp5(2) =
b. 10x        = ;       exp(x)
c.  5x =3D 25        = ;   exp(x) =3D 25
We called this exponent 2 as “the log (logarithm) of 25 in base 5”, and write this relation as 2 =3D log5(25).
In general if b= x =3D y, we called the exponent x as =
“ t= he log of y in base b” and write it as x =3D logb(y).<= /span>
The Logarithmic Functions
In part c= , since 52 =3D 25, the exponent x must be 2.<= /div>
In other words, the output “logb(y)” is “an exponent x”, where x is the exponent needed (in base b) to get y. 
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The Logarithmic Functions
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
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The Logarithmic Functions
The expressions expb(x) =3D y= and x =3D logb(y) describe the same = relation between the base b, the exponent x, and y.
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0226.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0227.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0228.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16<= /span>
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0229.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16 = à   2 =3D log4(16)=
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0230.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16 = à   2 =3D log4(16)
b.  w =3D u2+v = or w =3D expu(2 + v)
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0231.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16 = à   2 =3D log4(16)
b.  w =3D u2+v = or w =3D expu(2 + v) à log(w) =3D 2+v=
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0232.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example C:<= span style=3D'mso-spacerun:yes'>  Rewrite the log-form into the exp-form.
a. log3(1/9) =3D -2
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16 = à   2 =3D log4(16)
b.  w =3D u2+v = or w =3D expu(2 + v) à log(w) =3D 2+v=
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0233.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example C:<= span style=3D'mso-spacerun:yes'>  Rewrite the log-form into the exp-form.
a. log3(1/9) =3D -2 à 1/9 =3D exp3(-2) or 1/9= =3D 3-2 =
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16 = à   2 =3D log4(16)
b.  w =3D u2+v = or w =3D expu(2 + v) à log(w) =3D 2+v=
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0234.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example C:<= span style=3D'mso-spacerun:yes'>  Rewrite the log-form into the exp-form.
a. log3(1/9) =3D -2 à 1/9 =3D exp3(-2) or 1/9= =3D 3-2 =
b. 2w =3D l= ogv(a – b)
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16 = à   2 =3D log4(16)
b.  w =3D u2+v = or w =3D expu(2 + v) à log(w) =3D 2+v=
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
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The Logarithmic Functions
The expressions expb(x) =3D y and x =3D logb(y) describe the same relation betw= een the base b, the exponent x, and y. =
The expression expb(x) =3D y is called the exp-form and the expre= ssion logb(y) =3D x is called the log-form.
Example C:<= span style=3D'mso-spacerun:yes'>  Rewrite the log-form into the exp-form.
a. log3(1/9) =3D -2 à 1/9 =3D exp3(-2) or 1/9= =3D 3-2 =
b. 2w =3D l= ogv(a – b)=   à a – = b =3D expv(2w)= or a – b =3D v2w
Example B:<= span style=3D'mso-spacerun:yes'>  Rewrite the exp-form into the log-form.
a. 4= 2  = =3D 16 or exp4(2) =3D 16 = à   2 =3D log4(16)
b.  w =3D u2+v = or w =3D expu(2 + v) à log(w) =3D 2+v=
 expb(x) =3D y
if and only if
 x =3D logb(y)
Hence
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The Logarithmic Functions
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0.
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The Logarithmic Functions
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
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Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
Graphs of the Logarithmic Functions
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Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
 8
 4
 2
 1
1/2
1/4
x
y=3Dlog2<= span lang=3DEN-US style=3D'mso-fareast-language:ZH-CN'>(x)
Graphs of the Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0209_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZQC4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABk ALcAgAAAAAAAAAL/jI+py+0P4wO02oszDrr7D35ISGZciabgqJZnC8NsLNI2Ot+mznt5X3kBh4Df UEjsGYHIpG6pdB4P0mJVSZU2r7Ksc8tVQXngMM6bLJtJ4+ea1r6p3yI0cU7vxG34vMl+5CcGyCSY sgdneGZQ1adIgRjj+Bgp88hGGHW5kkm2ycmo9VkX+jXq0+l2qiHR6voKG5vQuMqaKlf7V5qWu3HL 13tR2TKpOCwWbHF8mBz0m9hc9CwZLb17V72Mkz1tGa3twn0d+N1NLF6MXD5euJ7O7E4bLzpvWs97 j51P3gzOhi6vnzl1AtlpKvhu2752CGU5fAhRQsBk/kIkzFNxBUB6/wgnBstYY+FBigPhdeRI0qAn kStP2nOJD6Y+mfxSXvzHUhVNhjY99gLpY+PLnig/llS4c6RRlTqJDl1606LQmE6pQo2INStWn7mA 6pk6s2pYqFxreWUFtibZoj+PhsuJCy4wudCSthSrti3TuHabrn2qN6pGutQIe+vLFy/Pv1YDl111 dofhc5MJKlbqmG1XrZw7x3p8KvKGtIszA968dy5i1ZfvMh5rujFqwSFX123tNzbs2aBHiRZGGjNv zWbd4rRdGPlh3Ilf5x1+unjq285LQ5ctnXbQyiaZs77qObx4Bb0//VYW3LXu59nLbzofJH3u67vb E4dsXCp3pN6przi3bl90+E2XXH8FVidcgNgNqN1X+72lHGURWoagevSxx6B7l8AHiXzN/ZdghveF Nl6JJp6IYlYFAAA7 ------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0205.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
 8
 4
 2
 1
1/2
  -2
1/4
x
y=3Dlog2<= span lang=3DEN-US style=3D'mso-fareast-language:ZH-CN'>(x)
Graphs of the Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0205_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZQC4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABk ALcAgAAAAAAAAAL/jI+py+0P4wO02oszDrr7D35ISGZciabgqJZnC8NsLNI2Ot+mznt5X3kBh4Df UEjsGYHIpG6pdB4P0mJVSZU2r7Ksc8tVQXngMM6bLJtJ4+ea1r6p3yI0cU7vxG34vMl+5CcGyCSY sgdneGZQ1adIgRjj+Bgp88hGGHW5kkm2ycmo9VkX+jXq0+l2qiHR6voKG5vQuMqaKlf7V5qWu3HL 13tR2TKpOCwWbHF8mBz0m9hc9CwZLb17V72Mkz1tGa3twn0d+N1NLF6MXD5euJ7O7E4bLzpvWs97 j51P3gzOhi6vnzl1AtlpKvhu2752CGU5fAhRQsBk/kIkzFNxBUB6/wgnBstYY+FBigPhdeRI0qAn kStP2nOJD6Y+mfxSXvzHUhVNhjY99gLpY+PLnig/llS4c6RRlTqJDl1606LQmE6pQo2INStWn7mA 6pk6s2pYqFxreWUFtibZoj+PhsuJCy4wudCSthSrti3TuHabrn2qN6pGutQIe+vLFy/Pv1YDl111 dofhc5MJKlbqmG1XrZw7x3p8KvKGtIszA968dy5i1ZfvMh5rujFqwSFX123tNzbs2aBHiRZGGjNv zWbd4rRdGPlh3Ilf5x1+unjq285LQ5ctnXbQyiaZs77qObx4Bb0//VYW3LXu59nLbzofJH3u67vb E4dsXCp3pN6przi3bl90+E2XXH8FVidcgNgNqN1X+72lHGURWoagevSxx6B7l8AHiXzN/ZdghveF Nl6JJp6IYlYFAAA7 ------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0206.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
 8
 4
 2
 1
  -1
1/2
  -2
1/4
x
y=3Dlog2<= span lang=3DEN-US style=3D'mso-fareast-language:ZH-CN'>(x)
Graphs of the Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0206_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZQC4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABk ALcAgAAAAAAAAAL/jI+py+0P4wO02oszDrr7D35ISGZciabgqJZnC8NsLNI2Ot+mznt5X3kBh4Df UEjsGYHIpG6pdB4P0mJVSZU2r7Ksc8tVQXngMM6bLJtJ4+ea1r6p3yI0cU7vxG34vMl+5CcGyCSY sgdneGZQ1adIgRjj+Bgp88hGGHW5kkm2ycmo9VkX+jXq0+l2qiHR6voKG5vQuMqaKlf7V5qWu3HL 13tR2TKpOCwWbHF8mBz0m9hc9CwZLb17V72Mkz1tGa3twn0d+N1NLF6MXD5euJ7O7E4bLzpvWs97 j51P3gzOhi6vnzl1AtlpKvhu2752CGU5fAhRQsBk/kIkzFNxBUB6/wgnBstYY+FBigPhdeRI0qAn kStP2nOJD6Y+mfxSXvzHUhVNhjY99gLpY+PLnig/llS4c6RRlTqJDl1606LQmE6pQo2INStWn7mA 6pk6s2pYqFxreWUFtibZoj+PhsuJCy4wudCSthSrti3TuHabrn2qN6pGutQIe+vLFy/Pv1YDl111 dofhc5MJKlbqmG1XrZw7x3p8KvKGtIszA968dy5i1ZfvMh5rujFqwSFX123tNzbs2aBHiRZGGjNv zWbd4rRdGPlh3Ilf5x1+unjq285LQ5ctnXbQyiaZs77qObx4Bb0//VYW3LXu59nLbzofJH3u67vb E4dsXCp3pN6przi3bl90+E2XXH8FVidcgNgNqN1X+72lHGURWoagevSxx6B7l8AHiXzN/ZdghveF Nl6JJp6IYlYFAAA7 ------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0207.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
 8
 4
 2
   0
 1
  -1
1/2
  -2
1/4
x
y=3Dlog2<= span lang=3DEN-US style=3D'mso-fareast-language:ZH-CN'>(x)
Graphs of the Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0207_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZQC4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABk ALcAgAAAAAAAAAL/jI+py+0P4wO02oszDrr7D35ISGZciabgqJZnC8NsLNI2Ot+mznt5X3kBh4Df UEjsGYHIpG6pdB4P0mJVSZU2r7Ksc8tVQXngMM6bLJtJ4+ea1r6p3yI0cU7vxG34vMl+5CcGyCSY sgdneGZQ1adIgRjj+Bgp88hGGHW5kkm2ycmo9VkX+jXq0+l2qiHR6voKG5vQuMqaKlf7V5qWu3HL 13tR2TKpOCwWbHF8mBz0m9hc9CwZLb17V72Mkz1tGa3twn0d+N1NLF6MXD5euJ7O7E4bLzpvWs97 j51P3gzOhi6vnzl1AtlpKvhu2752CGU5fAhRQsBk/kIkzFNxBUB6/wgnBstYY+FBigPhdeRI0qAn kStP2nOJD6Y+mfxSXvzHUhVNhjY99gLpY+PLnig/llS4c6RRlTqJDl1606LQmE6pQo2INStWn7mA 6pk6s2pYqFxreWUFtibZoj+PhsuJCy4wudCSthSrti3TuHabrn2qN6pGutQIe+vLFy/Pv1YDl111 dofhc5MJKlbqmG1XrZw7x3p8KvKGtIszA968dy5i1ZfvMh5rujFqwSFX123tNzbs2aBHiRZGGjNv zWbd4rRdGPlh3Ilf5x1+unjq285LQ5ctnXbQyiaZs77qObx4Bb0//VYW3LXu59nLbzofJH3u67vb E4dsXCp3pN6przi3bl90+E2XXH8FVidcgNgNqN1X+72lHGURWoagevSxx6B7l8AHiXzN/ZdghveF Nl6JJp6IYlYFAAA7 ------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0208.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
 8
 4
   1
 2
   0
 1
  -1
1/2
  -2
1/4
x
y=3Dlog2<= span lang=3DEN-US style=3D'mso-fareast-language:ZH-CN'>(x)
Graphs of the Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0208_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZQC4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABk ALcAgAAAAAAAAAL/jI+py+0P4wO02oszDrr7D35ISGZciabgqJZnC8NsLNI2Ot+mznt5X3kBh4Df UEjsGYHIpG6pdB4P0mJVSZU2r7Ksc8tVQXngMM6bLJtJ4+ea1r6p3yI0cU7vxG34vMl+5CcGyCSY sgdneGZQ1adIgRjj+Bgp88hGGHW5kkm2ycmo9VkX+jXq0+l2qiHR6voKG5vQuMqaKlf7V5qWu3HL 13tR2TKpOCwWbHF8mBz0m9hc9CwZLb17V72Mkz1tGa3twn0d+N1NLF6MXD5euJ7O7E4bLzpvWs97 j51P3gzOhi6vnzl1AtlpKvhu2752CGU5fAhRQsBk/kIkzFNxBUB6/wgnBstYY+FBigPhdeRI0qAn kStP2nOJD6Y+mfxSXvzHUhVNhjY99gLpY+PLnig/llS4c6RRlTqJDl1606LQmE6pQo2INStWn7mA 6pk6s2pYqFxreWUFtibZoj+PhsuJCy4wudCSthSrti3TuHabrn2qN6pGutQIe+vLFy/Pv1YDl111 dofhc5MJKlbqmG1XrZw7x3p8KvKGtIszA968dy5i1ZfvMh5rujFqwSFX123tNzbs2aBHiRZGGjNv zWbd4rRdGPlh3Ilf5x1+unjq285LQ5ctnXbQyiaZs77qObx4Bb0//VYW3LXu59nLbzofJH3u67vb E4dsXCp3pN6przi3bl90+E2XXH8FVidcgNgNqN1X+72lHGURWoagevSxx6B7l8AHiXzN/ZdghveF Nl6JJp6IYlYFAAA7 ------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0204.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
   3
 8
   2
 4
   1
 2
   0
 1
  -1
1/2
  -2
1/4
x
y=3Dlog2<= span lang=3DEN-US style=3D'mso-fareast-language:ZH-CN'>(x)
Graphs of the Logarithmic Functions
------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0204_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZQC4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABk ALcAgAAAAAAAAAL/jI+py+0P4wO02oszDrr7D35ISGZciabgqJZnC8NsLNI2Ot+mznt5X3kBh4Df UEjsGYHIpG6pdB4P0mJVSZU2r7Ksc8tVQXngMM6bLJtJ4+ea1r6p3yI0cU7vxG34vMl+5CcGyCSY sgdneGZQ1adIgRjj+Bgp88hGGHW5kkm2ycmo9VkX+jXq0+l2qiHR6voKG5vQuMqaKlf7V5qWu3HL 13tR2TKpOCwWbHF8mBz0m9hc9CwZLb17V72Mkz1tGa3twn0d+N1NLF6MXD5euJ7O7E4bLzpvWs97 j51P3gzOhi6vnzl1AtlpKvhu2752CGU5fAhRQsBk/kIkzFNxBUB6/wgnBstYY+FBigPhdeRI0qAn kStP2nOJD6Y+mfxSXvzHUhVNhjY99gLpY+PLnig/llS4c6RRlTqJDl1606LQmE6pQo2INStWn7mA 6pk6s2pYqFxreWUFtibZoj+PhsuJCy4wudCSthSrti3TuHabrn2qN6pGutQIe+vLFy/Pv1YDl111 dofhc5MJKlbqmG1XrZw7x3p8KvKGtIszA968dy5i1ZfvMh5rujFqwSFX123tNzbs2aBHiRZGGjNv zWbd4rRdGPlh3Ilf5x1+unjq285LQ5ctnXbQyiaZs77qObx4Bb0//VYW3LXu59nLbzofJH3u67vb E4dsXCp3pN6przi3bl90+E2XXH8FVidcgNgNqN1X+72lHGURWoagevSxx6B7l8AHiXzN/ZdghveF Nl6JJp6IYlYFAAA7 ------=_NextPart_01C957DA.8B716000 Content-Location: file:///C:/4D764A33/2TheLogarithmFunctions_files/slide0210.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Introduction to Logarithm
Since bx =3D y is positive for = all x's, so the domain of logb(y) is the set of all y > 0. In the following discussio= n, we will switch back to using x as the input variable and write the log-function as logb(x).
The Logarithmic Functions
(1, 0)=
(2, 1)=
(4, 2)=
(8, 3)=
(16, 4)
(1/2, -1)
(1/4, -2)
y=3Dlog2(x)<= /div>
   3
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 1
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1/2
  -2
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x
y=3Dlog2<= span lang=3DEN-US style=3D'mso-fareast-language:ZH-CN'>(x)
Graphs of the Logarithmic Functions
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