Question

In the following exercises, solve each equation.

$6^{4x-17}=216$

Short answer

On solving the equation, we get $x=6$.

Step-by-step solution

Step 1. Given information.

Consider the given exponential equation,

$6^{4x-17}=216$

Write both sides of the equation with the same base,

$6^{4x-17}=6^3$

Write a new equation by setting the exponents equal,

$4x-17=3$

On solving the equation,

$$\begin{gathered} 4x-17+17=3+17 \\ 4x=20 \\ x=5 \end{gathered}$$

Step 2. Check the answers.

Substitute $x=5$in the original equation,

$$\begin{gathered} 6^{4\left(5\right)-17}=216 \\ {6}^{20-17}=216 \\ {6}^3=216 \\ 216=216 \end{gathered}$$

This is true.