# How do you solve the exponential equation 8^(5x)=16^(3x+4)?

Mar 8, 2017

$\implies x = \frac{16}{3}$

#### Explanation:

${8}^{5 x} = {16}^{3 x + 4}$

$\implies {\left({2}^{3}\right)}^{5 x} = {\left({2}^{4}\right)}^{3 x + 4}$

$\implies {2}^{15 x} = {2}^{4 \left(3 x + 4\right)}$

$\implies 15 x = 12 x + 16$

$\implies x = \frac{16}{3}$