#### Answer

$x=3+\dfrac{\log12}{2\log5}\approx3.7720$

#### Work Step by Step

$5^{2x-6}=12$
Apply $\log$ to both sides of the equation:
$\log5^{2x-6}=\log12$
Take $2x-6$ down to multiply in front of its respective $\log$:
$(2x-6)\log5=\log12$
Solve for $x$:
$2x-6=\dfrac{\log12}{\log5}$
$2x=6+\dfrac{\log12}{\log5}$
$x=\dfrac{6+\dfrac{\log12}{\log5}}{2}$
$x=3+\dfrac{\log12}{2\log5}\approx3.7720$