Question

In the following exercises, solve each equation:

$3^{x+3}=9$

Short answer

The solution of the given equation is$-1.$

Step-by-step solution

Step 1. Given Information

The given equation is$3^{x+3}=9.$

We have to solve it.

Step 2. Solve the equation 

To solve the equation, write both sides of the equation with the same base.

So,$3^{x+3}=3^2.$

Now, write a new equation by setting the exponents equal.

$$\begin{gathered} x+3=2 \\ x=2-3 \\ x=-1 \end{gathered}$$

Step 3. Verify the solution 

To verify the solution, substitute $x=-1$in the original equation.

$$\begin{gathered} 3^{-1+3}=9 \\ {3}^2=9 \\ 9=9 \end{gathered}$$

Hence, our result is true.