# How do you solve log_3 32 = x?

Nov 27, 2015

This is already 'solved' in that $x = {\log}_{3} 32$

but you can use the change of base formula to find:

$x = \log \frac{32}{\log} \left(3\right) = \ln \frac{32}{\ln} \left(3\right) \approx 3.15465$

#### Explanation:

The change of base formula tells use that if $a , b , c > 0$ then:

${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$

This allows us to express ${\log}_{3} 32$ in terms of common (base $10$) logarithms or natural (base $e$) logarithms:

${\log}_{3} 32 = \log \frac{32}{\log} \left(3\right) = \ln \frac{32}{\ln} \left(3\right) \approx 3.15465$