1. Properties of Logarithm
Logarithmic Funcitons

2. Review: Evaluating exponents

3. loga x = y a y = x Logarithims
A logarithmic function is the inverse function of an exponential function.
loga x = y a y = x

4. loga x = y log2 8 = 3 Read as : “logarithm of x with base a equals y”
“logarithm of 8 with base 2 equals 3”

5. Logarithms Convert each of the following to a logarithmic equation.
Convert each of the following to a exponential Function:
a) log2 4 = m b) log5 w = 9
59 = w
2m = 4
Convert each of the following to a logarithmic equation.
a) 25 = 5x b) ew = 30
log5 25 = x loge 30 = w

6. Evaluating Logarithms
Example1: log5 x = 2
5 2= x
Change the logarithmic to exponential function:
log5 x = 2
25 = x

7. Evaluating Logarithms
Example1: logb 64 = 3
b 3= 64
Change the logarithmic to exponential function:
logb 64 = 3
b = 4

8. Evaluating Logarithms
Example1: log3 7 = y
3 y= 7
Change the logarithmic to exponential function:
log3 7 = y

9. Equivalent Exponential Equation
Examples: Write the equivalent exponential equation and solve for y.
Solution
Equivalent Exponential Equation
Logarithmic Equation
y = log216
16 = 2y
y = 4
y = log2( )
= 2 y
y = –1 9
y = log416
16 = 4y
y = 2
y = log51
1 = 5 y
y = 0