# How do you solve for x?: log_6 (36) = 5x + 3

Oct 21, 2015

$x = - \frac{1}{5}$

#### Explanation:

Using the definition of logs, together with laws of exponents, we may write this equation in exponential form as

${6}^{5 x + 3} = 36$

$\therefore {6}^{5 x} \cdot {6}^{3} = {6}^{2}$

$\therefore 5 x + 3 = 2 \implies - \frac{1}{5}$