Question

In the following exercises, solve each equation:

$2^{3x-8}=16$

Short answer

The solution of the given equation is$4.$

Step-by-step solution

Step 1. Given Information

The given equation is $2^{3x-8}=16.$

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, $2^{3x-8}=2^4$

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

$$\begin{gathered} 3x-8=4 \\ 3x=4+8 \\ 3x=12 \\ x=4 \end{gathered}$$

Step 3. Verify the solution

To verify the solution, substitute $x=4$in the original equation.

role="math" localid="1644922900843" $$\begin{gathered} 2^{3\left(4\right)-8}=16 \\ {2}^{12-8}=16 \\ {2}^4=16 \\ 16=16 \end{gathered}$$

Hence, our result is true.