Answer
$x =\dfrac{\frac{\log{12}}{\log{5}}+6}{2} \approx 3.7720$
Work Step by Step
Take the common logarithm of both sides to have:
$\log{(5^{2x-6})}=\log{12}$
Apply the power rule to have:
$(2x-6)\log{5}=\log{12}$
Divide $\log{5}$ to both sides to have:
$2x-6=\dfrac{\log{12}}{\log{5}}
\\2x=\dfrac{\log{12}}{\log{5}}+6
\\x =\dfrac{\frac{\log{12}}{\log{5}}+6}{2} \approx 3.7720$
