# How do you express log_3 8 in terms of common logarithms?

Mar 7, 2018

$x = \log \frac{8}{\log} 3$

#### Explanation:

Let ${\log}_{3} 8 = x$, then we know that ${3}^{x} = 8$

Now taking common log (to base $10$) on both sides, we get

$x \log 3 = \log 8$

or $x = \log \frac{8}{\log} 3 = \frac{0.9031}{0.4771} = 1.8929$

Note that ${\log}_{a} b = \log \frac{b}{\log} a$