# How do you evaluate #log_5 92#?

##### 2 Answers

#### Explanation:

There is a property in logarithms which is *The proof for this is at the bottom of the answer* Using this rule:

Which if you type into a calculator you'll get approximately 2.81.

Proof:

Let

Therefore

#### Explanation:

As an example consider

This mat be written as:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Given:

Let

The we have:

You can use log base 10 or natural loges (ln). This will work for either.

Take logs of both sides

Write this as:

Divide both sides by