![Page 1: Definition of Logarithms We recall from the last lesson that a logarithm is defined as y = log b x if and only if B y = x. We will use this definition](https://reader030.vdocuments.net/reader030/viewer/2022032802/56649de85503460f94ae220f/html5/thumbnails/1.jpg)
![Page 2: Definition of Logarithms We recall from the last lesson that a logarithm is defined as y = log b x if and only if B y = x. We will use this definition](https://reader030.vdocuments.net/reader030/viewer/2022032802/56649de85503460f94ae220f/html5/thumbnails/2.jpg)
Definition of LogarithmsWe recall from the last lesson that a logarithm is defined
as y = logbx if and only if By = x.
We will use this definition to solve equations involving logarithmic functions.
So…
3 = log7 x 73 = x
2 = logx 25 x2 = 25
y = log4 16 4y = 16
And…
62 = x 2 = log6 x
x3 = 8 3 = logx 8
8y = 64 y = log8 64
![Page 3: Definition of Logarithms We recall from the last lesson that a logarithm is defined as y = log b x if and only if B y = x. We will use this definition](https://reader030.vdocuments.net/reader030/viewer/2022032802/56649de85503460f94ae220f/html5/thumbnails/3.jpg)
Rewriting Logarithms You can use the log properties to solve equations when the variable is contained in a logarithm.
1. Use the logarithm properties to rewrite as one log.
2. Rewrite the log into exponential form.
3. Solve • Raise 2 to the 5th
power• Distribute• Add 4 to both sides• Divide by the
coefficient
2 2
2
5
log 1 log 4 5
log 4 1 5
2 4 1
32 4 4
36 4
9
x
x
x
x
x
x
![Page 4: Definition of Logarithms We recall from the last lesson that a logarithm is defined as y = log b x if and only if B y = x. We will use this definition](https://reader030.vdocuments.net/reader030/viewer/2022032802/56649de85503460f94ae220f/html5/thumbnails/4.jpg)
Equations with Natural LogsUse the same method when working with ln.
2
2
ln 1 1 3
ln 1 2
1
1
x
e
e
x
x
x
1.Isolate the ln
2.Rewrite in exponential form
Remember, natural logs have a base of e
3.Isolate variable
![Page 5: Definition of Logarithms We recall from the last lesson that a logarithm is defined as y = log b x if and only if B y = x. We will use this definition](https://reader030.vdocuments.net/reader030/viewer/2022032802/56649de85503460f94ae220f/html5/thumbnails/5.jpg)
Application of LogarithmsIn 1906, San Francisco suffered a magnitude 7.8 (by many estimates) earthquake that caused unthinkable damage to the city.
To read more details about the quake go to:http://en.wikipedia.org/wiki/1906_San_Francisco_earthquake
The magnitude of an earthquake can be calculated using the
function y = log(1000x), where x represents the seismographic
reading 100 km from the center of the quake. What was the
Seismographic reading, in mm, for this earthquake?
![Page 6: Definition of Logarithms We recall from the last lesson that a logarithm is defined as y = log b x if and only if B y = x. We will use this definition](https://reader030.vdocuments.net/reader030/viewer/2022032802/56649de85503460f94ae220f/html5/thumbnails/6.jpg)
Application of Logs, con’t1. Identify
variables
2. Sub in values3. Rewrite in
exponential form4. Isolate the
variable
10
7.8
7.8 log 1000
10 1000
63095734.45 1000
63095.73 mm
x
x
x
x
y= 7.8
y = log(1000x)
The seismographic reading 100 km from the center of the quake is ≈ 63,096 mm.
![Page 7: Definition of Logarithms We recall from the last lesson that a logarithm is defined as y = log b x if and only if B y = x. We will use this definition](https://reader030.vdocuments.net/reader030/viewer/2022032802/56649de85503460f94ae220f/html5/thumbnails/7.jpg)
Additional Resourceshttp://math.usask.ca/emr/menu_exp.html
http://www.purplemath.com/modules/solvelog.htm
http://www.purplemath.com/modules/solvelog2.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut46_logeq.htm
http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=age&wcsuffix=0805