Question

How do you solve `log_10 30`?

Answer 1

`1.4771`

Explanation:

You could just plug this into a calculator as `log30`.

Note that the `log` button on a calculator implies a base of `10`, so typing `log30` is the same as `log_10 30`.

This gives `log_10 30=1.4771`

Another way to simplify this is to write `30` as `10xx3`.

`log_10 30=log_10 ((10)3)`

Use log rules to expand this: `log_c(ab)=log_ca+log_cb`

`log_10 30=log_10 10+log_10 3`

Since `log_10 10=1`,

`log_10 30=1+log_10 3`