# How do you solve 5^x + 4(5^(x+1)) = 63?

Dec 16, 2015

$x = {\log}_{5} \left(3\right)$

#### Explanation:

Given:
$\textcolor{w h i t e}{\text{XXX}} {5}^{x} + 4 \left({5}^{x + 1}\right) = 63$

Extract the common factor of ${5}^{x}$ from both terms on the left side:
$\textcolor{w h i t e}{\text{XXX}} {5}^{x} \left(1 + 4 \left({5}^{1}\right)\right) = 63$
Simplify the numeric expression
$\textcolor{w h i t e}{\text{XXX}} {5}^{x} \left(21\right) = 63$
Divide both sides by $21$
$\textcolor{w h i t e}{\text{XXX}} {5}^{x} = 3$
Apply the equivalence: ${\log}_{b} a = c \Leftrightarrow {b}^{c} = a$
$\textcolor{w h i t e}{\text{XXX}} x = {\log}_{5} \left(3\right)$