# How do you solve 5(4^36)=4^x?

May 7, 2016

$x = 37.161$

#### Explanation:

$5 \left({4}^{36}\right) = {4}^{x}$ means

x=log_4(5(4^36) or

$x = {\log}_{4} \left(5\right) + {\log}_{4} \left({4}^{36}\right)$ or

$x = {\log}_{4} \left(5\right) + 36 {\log}_{4} \left(4\right)$ or

$x = {\log}_{4} 5 + 36$ or

$x = \log \frac{5}{\log} 4 + 36 = 1.161 + 36 = 37.161$

May 9, 2016

Use laws of indices first, then logs.
$37.61 = x$

#### Explanation:

There are powers of 4 on both sides of the equation.

$5 \left({4}^{36}\right) = {4}^{x} \text{ divide by} {4}^{36}$

$5 = \frac{{4}^{x}}{4} ^ 36 \text{ subtract indices}$

$5 = {4}^{x - 36}$

$\log 5 = \left(x - 36\right) \log 4$

$\log \frac{5}{\log} 4 = x - 36$

$1.6096 = x - 36$

$37.61 = x$