Question

In the following exercises, solve each equation.

$3^{3x+1}=81$

Short answer

On solving the equation, we get $x=1$.

Step-by-step solution

Step 1. Given information.

Consider the given exponential equation,

$3^{3x+1}=81$

Write both sides of the equation with the same base,

$3^{3x+1}=3^4$

Write a new equation by setting the exponents equal,

$3x+1=4$

On solving the equation,

$$\begin{gathered} 3x+1-1=4-1 \\ 3x=3 \\ x=1 \end{gathered}$$

Step 2. Check the answers.

Substitute $x=1$in the original equation,

$$\begin{gathered} 3^{3\left(1\right)+1}=81 \\ {3}^{3+1}=81 \\ {3}^4=81 \\ 81=81 \end{gathered}$$

This is true.