Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 475: 72

$x = 1$

Rewrite the terms so they share a common base (note that $125=5^3$): $5^{3x} = 5^{3}$ If two numbers having the same base are equal, that means that their exponents are also the same, so set the exponents equal to one another to solve for $x$: $3x = 3$ Divide both sides of the equation by $3$: $x = 1$