Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Chapter Test - Page 372: 14


$x=1$ or The solution set is: $\{1\}$.

Work Step by Step

The term $125$ can be written as: $125=5^3$ So, the given equation can be equivalent to $5^{x+2}=5^3$ Recall the rule that $a^m=a^n \longrightarrow m=n$ if $a\ne1,a\ne-1$ Applying this rule, we obtain: $5x+2=5^3 \\ x +2=3$ Simplify this equation to obtain: $x+2=3 \\ (x+2)−2=3−2 \\ x=1$ So, the solution set is: $\{1\}$
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