# How do you find the value of log_2 8 using the change of base formula?

Nov 13, 2016

The change of base formula states:

$\textcolor{g r e e n}{{\log}_{n} \left(a\right) = \log \frac{a}{\log} n}$

So:

${\log}_{2} \left(8\right)$

$\implies \log \frac{8}{\log} 2$

Write in powers of $2$.

$\implies \frac{\log {2}^{3}}{\log {2}^{1}}$

Use the rule $\log {n}^{a} = a \log n$.

$\implies \frac{3 \log 2}{1 \log 2}$

$\implies 3$

Hopefully this helps!