1. 8-5 Exponential and Logarithmic Equations
Obj: To be able to solve exponential and logarithmic equations.

2. Solving an Exponential Equation
Example 1
Solve.
62x = 21
log 62x = log 21
x∙2 log 6 = log 21
2x log 6 = log 21
x = log 21 ≈
2 log 6

3. logbM = logcM logcb Change of Base Formula
For any positive numbers, M, N, and c, with b≠1 and c≠1.
logbM = logcM
logcb
This is used to get any logarithm back to base 10 to evaluate!

4. Evaluate using Change of Base Formula
Example 2
Evaluate.
log48
= log 8
= 1.5
log 4
Use the change of base formula to get to base 10!

5. Solving an Exponential Equation by Changing Bases
Example 3
Solve.
75x = 3000
Use the change of base formula to get back to base 10!
log775x = log73000
5x = log73000
5x = log 3000 ≈
log 7

6. Solving an Exponential Equation by Graphing
Example 4
Solve.
116x = 786
Step 1: Graph TWO equations.
y = 116x
y = 786
Step 2: Find the point of intersection.
x ≈

7. Solving a Logarithmic Equation
Example 5
Solve.
log(7 – 2x) = -1
Step 1: Write in exponential form.
Base 10!
7 – 2x = 10-1
Step 2: Solve for x.
7 – 2x = .1
– 2x = -6.9
x = 3.45

8. Using Properties to Solve an Equation
Example 6
Solve.
log 6 – log 3x = -2
Step 1: Write as a single logarithm.
log (6/3x) = -2
Step 2: Write in exponential form.
6/3x = 10-2

9. Using Properties to Solve an Equation
Example 6
Solve.
log 6 – log 3x = -2
Step 3: Solve for x.
6/3x = 10-2
= 1/100
x = 200
3x/6 = 100
3x = 600
Take reciprocal of both sides!

10. Homework
p. 456 #1 – 47 every other odd