# Solve the equation. 4^{x-3}=16

Solve the equation. ${4}^{x-3}=16$
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Step 1
We have to solve the equation:
${4}^{x-3}=16$
Rewriting the equation,
${4}^{x-3}=16$
$=4×4$
${4}^{x-3}={4}^{2}$
We know that
If ${a}^{m}={a}^{n}$ then m=n.
Step 2
Therefore for the given condition,
${4}^{x-3}={4}^{2}$
We can write,
$x-3=2$
$x=2+3$
$=5$
Hence, solution of the equation is x=5.