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

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

Concept

You need to find x for the logarithmic equation. Solve a Logarithmic Equation Solve log4 x 2 = log4 (–6x – 8). A. 4 B. 2 C. –4, –2 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

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 = –4 x = –2 Solve each equation. Example 2

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

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