Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 473: 10

$x=-1$

Note that $\frac{1}{125}=5^{-3}$ so the given equation is equivalent to: $5^{3x}=5^{-3}$ Using the rule $a^m=a^n\longrightarrow m=n$ gives: $5^{3x}=5^{-3}$ $3x=-3$ $x=-1$ Check: $5^{3*-1}=\frac{1}{125}$ $5^{-3}=\frac{1}{125}$ $\frac{1}{125}=\frac{1}{125}$ Thus, we have confirmed that the answer is correct.