Answer
$x=2+\dfrac{\log12}{\log8}\approx3.1950$
Work Step by Step
$8^{x-2}=12$
Apply $\log$ to both sides of the equation:
$\log8^{x-2}=\log12$
Take $x-2$ down to multiply in front of its respective $\log$:
$(x-2)\log8=\log12$
Solve for $x$:
$x-2=\dfrac{\log12}{\log8}$
$x=2+\dfrac{\log12}{\log8}\approx3.1950$
