## 12.8.1 Introduction to Logarithms

Logarithms are a way of algebraically dealing with variables that are in the exponents of functions.  They are a kind of notation that was developed to deal with the inverse of exponential functions.  Learn more about logarithms, how they are related to exponential functions and the restrictions on values of logarithms.

Resources:

• Notes

Assignment:

• p380 #1-18, C1 *21,22

Things you should know after today:

• what does a logarithm represent?
• how to write a logarithm in exponential form
• how to write an exponent as a logarithm
• the restrictions on logarithms and exponents
• the graph of a logarithm
• domain
• range
• the equation for the asymptote
• the y-intercept

## 12.8.2 Transforming Graphs of Logarithmic Functions

A logarithmic function can be transformed the same way as all of the other functions we've looked at so far.  We will consider drawing the graphs of logarithmic functions in a few different ways, and then use the coordinates we've generated for these functions to draw transformed graphs.

Resources;

• Notes
• Notes: The Natural Logarithm

Assignment:

• p389 #1, 3-7, 11-14, C1, C2 *15, *16

Things you should know after today:

• How changing the base is related to a horizontal stretch
• how transformations affect graphs of logarithms

## 12.8.4 Solving Logarithmic Equations

There are two strategies for solving logarithmic equations.  Today, you will find out how each can be used.

Resources

• Notes: Part A
• Notes: Part B

Assignment

• p412 #1, 3-6, 8-10, *19-21

Things you should know how to do after today:

• Use laws of logarithms to help you solve equations involving logarithms
• Use the definition of a logarithm to help solve equations of the form:
• Solve equations of the form:
• Solve exponential equations using logarithms when:
• there are different bases that are not powers of a common base
• the variable is in the exponent
• Use an exponential equation where the variable is in the exponent to model problems and solve using logarithms