1. MAT 150 – Class #17 Topics: Graph and evaluate Logarithmic Functions
Convert equations to Logarithmic and Exponential Forms
Evaluate and Apply Common Logarithms
Evaluate and Apply Natural Logarithms
Apply Logarithmic Properties.

2. Graphing
Graph each of the following functions using a table of values. (Hint: The log button on your calculator assumes that it is with a base of 10)
𝑦= 10 𝑥 𝑦= log 10 𝑥
What do you notice about the two graphs?
Therefore, exponential functions and logarithmic functions are inverses (opposites) of each other.

3. Writing Logarithms in Exponential Form
Logarithmic
25 = 5²
729= 3 6
𝑦= 𝑏 𝑥
log 𝑏 𝑦 =𝑥

4. Some Properties of Logarithms
Property
Example
log 𝑏 𝑏 =1
log 𝑏 1 =0
log 𝑏 ( 𝑀𝑁 )= log 𝑏 𝑀+ log 𝑏 𝑁
log 𝑏 𝑀 𝑁 = log 𝑏 𝑀 − log 𝑏 𝑁
log 𝑏 𝑀 𝑥 =𝑥∙ log 𝑏 𝑀

5. Expanding Logarithms
Rewrite each of the following expressions as a sum, difference or product of logarithms and simplify if possible.
log 4 5(𝑥−7)
ln [ 𝑒 2 𝑒+3 ]
log 𝑥 −8 𝑥
log 4 𝑦 6
ln 1 𝑥 5

6. Single Logarithms
Rewrite each of the following expressions as a single logarithm.
log 3 𝑥 +4 log 3 𝑦 =
1 2 log 𝑎 −3 log 𝑏 =
ln 5𝑥 −3 ln 𝑧 =

7. Japan’s Population
The population of Japan for the years 1984 – 2006 is approximated by the logarithmic function 𝑦= ln 𝑥 million people, with x equal to the number of years after According to the model, what is the estimated population in 2000? In 2020?

8. Assignment Pg. 337-340 #1-11 odd #15-17 odd #31-32 #35-37 odd #39, 41
REMINDER:
TEST 3 DUE AT THE BEGINNING OF CLASS FRIDAY