# How do you solve 4^x=sqrt(5^(x+2))?

Nov 17, 2016

$x = \frac{2 \log \left(5\right)}{4 \log \left(2\right) - \log \left(5\right)}$

#### Explanation:

Squaring both sides

${4}^{2 x} = {5}^{2} {5}^{x}$ or
${16}^{x} = {5}^{x} {5}^{2}$ or
${\left(\frac{16}{5}\right)}^{x} = {5}^{2}$ now applying $\log$ to both sidexs
$x \left(\log \left(16\right) - \log \left(5\right)\right) = 2 \log \left(5\right)$ then
$x = \frac{2 \log \left(5\right)}{4 \log \left(2\right) - \log \left(5\right)}$