Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 473: 24

$x=1.2871$ See the graph below.

We are asked to solve the following problem by graphing: $5^{3x}=500$ We graph the left and right sides of the equation as two separate graphs ($y$ equations). We trace the point of intersection: $(1.2871,500)$. The $x$ value gives us the solution we are looking for.