Question

How can I solve for the logarithm?

Answer 1

$\bf 12^{2x-8}=15\\\\ -----------------------------\\\\ log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\impliedby thus\\\\ -----------------------------\\\\ log\left( 12^{2x-8} \right)=log(15)\implies (2x-8)log(12)=log(15) \\\\\\ 2x-8=\cfrac{log(15)}{log(12)}\implies 2x=\cfrac{log(15)}{log(12)}+8\implies x=\cfrac{\frac{log(15)}{log(12)}+8}{2}$