# How do you solve log_10 30?

Jan 21, 2016

$1.4771$

#### Explanation:

You could just plug this into a calculator as $\log 30$.

Note that the $\log$ button on a calculator implies a base of $10$, so typing $\log 30$ is the same as ${\log}_{10} 30$.

This gives ${\log}_{10} 30 = 1.4771$

Another way to simplify this is to write $30$ as $10 \times 3$.

${\log}_{10} 30 = {\log}_{10} \left(\left(10\right) 3\right)$

Use log rules to expand this: ${\log}_{c} \left(a b\right) = {\log}_{c} a + {\log}_{c} b$

${\log}_{10} 30 = {\log}_{10} 10 + {\log}_{10} 3$

Since ${\log}_{10} 10 = 1$,

${\log}_{10} 30 = 1 + {\log}_{10} 3$