Question

Solve the equation$2^{2x-4}=64$.

Short answer

On solving the equation, we get,

$x=5$

Step-by-step solution

Step 1. Given information.

Consider the given equation,

$2^{2x-4}=64$

Rewrite both sides with the same base,

role="math" localid="1645027330319" $2^{2x-4}=2^6$

As the base are same, so the exponents must be equal,

$2x-4=6$

Step 2. Solve the equation.

Add $4$on both sides,

role="math" localid="1645027416734" $$\begin{gathered} 2x-4+4=6+4 \\ 2x=10 \\ x=\frac{10}{2} \\ x=5 \end{gathered}$$

Step 3. Check the answer.

Substitute the value of xin the original equation,

$$\begin{gathered} 2^{2\left(5\right)-4}=64 \\ {2}^{10-4}=64 \\ {2}^6=64 \\ 64=64 \end{gathered}$$

This is true.