# How do you calculate log_5 (18)?

Apr 12, 2018

${\log}_{5} 18 = 1.7959$

#### Explanation:

Let ${\log}_{n} m = x$

then ${n}^{x} = m$ and taking log to the base $10$ on each side

$x \log n = \log m$ i.e. $x = \log \frac{m}{\log} n$

i.e. we can write ${\log}_{n} m = \log \frac{m}{\log} n$

or ${\log}_{5} 18 = \log \frac{18}{\log} 5 = \frac{1.2553}{0.6990} = 1.7959$