1. Definition of logarithm
Solve a Logarithmic Equation
Solve
Original equation
Definition of logarithm
8 = 23
Power of a Power
Answer: x = 16
Example 1

2. Solve A.
B. n = 3
C. n = 9 D.
n =
Example 1

3. Concept

4. You need to find x for the logarithmic equation.
Solve a Logarithmic Equation
Solve log4 x 2 = log4 (–6x – 8).
A B C. –4, – D. no solutions
Read the Test Item
You need to find x for the logarithmic equation.
Solve the Test Item
log4 x 2 = log4 (–6x – 8) Original equation
x 2 = (–6x – 8) Property of Equality for Logarithmic Functions
Example 2

5. x 2 + 6x + 8 = 0 Subtract (–6x – 8) from each side.
Solve a Logarithmic Equation
x 2 + 6x + 8 = 0 Subtract (–6x – 8) from each side.
(x + 4)(x + 2) = 0 Factor.
x + 4 = 0 or x + 2 = 0 Zero Product Property
x = – x = –2 Solve each equation.
Example 2

6. Substitute each value into the original equation.
Solve a Logarithmic Equation
Check
Substitute each value into the original equation.
x = –4 ?
log4 (–4)2 = log4 [–6(–4) – 8)]
log4 16 = log4 16 
x = –2 ?
log4 (–2)2 = log4 [–6(–2) – 8)]
log4 4 = log4 4 
Answer: The solutions are x = –4 and x = –2. The answer is C.
Example 2

7. Solve log4 x 2 = log4 (x + 20). A. 5 and –4 B. –2 and 10 C. 2 and –10
D. no solutions
Example 2