How do you evaluate log_4 32?

Jul 15, 2015

Use the change of base formula to get:

${\log}_{4} 32 = \frac{{\log}_{2} {2}^{5}}{{\log}_{2} {2}^{2}} = \frac{5}{2}$

Explanation:

In general, ${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$

$32 = {2}^{5}$ and $4 = {2}^{2}$

So ${\log}_{2} \left(32\right) = {\log}_{2} \left({2}^{5}\right) = 5$

and ${\log}_{2} \left(4\right) = {\log}_{2} \left({2}^{2}\right) = 2$

Hence ${\log}_{4} \left(32\right) = \frac{5}{2}$