Answer
$x=12$
Work Step by Step
The given equation is
$\Rightarrow 7^{x-4}=7^{8}$
Equate the exponents.
$\Rightarrow x-4=8$
Add $4$ to each side.
$\Rightarrow x-4+4=8+4$
Simplify.
$\Rightarrow x=12$
Check: $(x=12)$
$\Rightarrow 7^{12-4}=7^{8}$
$\Rightarrow 7^{8}=7^{8}$
True.
Hence, the solution is $x=12$.
