How do you solve 5^x = 10?

Feb 24, 2016

$x = {\log}_{5} 10 \approx 1.430677$

Explanation:

Make use of the standard relationship
$\textcolor{w h i t e}{\text{XXX}} {\log}_{b} a = c \iff {b}^{c} = a$
or (reversed)
$\textcolor{w h i t e}{\text{XXX}} {b}^{c} = a \iff {\log}_{b} a$

So
$\textcolor{w h i t e}{\text{XXX}} {5}^{x} = 10 \iff {\log}_{5} 10 = x$

${\log}_{5} 10$ can be evaluated using a calculator as $\approx 1.430677$