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

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