# How do you solve log5m = log5125?

Apr 2, 2018

See explanation.

#### Explanation:

First we have to clarify what the equation is.

• If the digit $5$ on both sides is the base then the equation should be written as:

## ${\log}_{5} m = {\log}_{5} 125$

The bases are equal, so you can change the $\log$ equation into the equation of expressions under $\log$ signs:

## $m = 125$

• However if the digit $5$ is the part of number under the $\log$ sign we have:

## $\log 5 m = \log 5125$

If a base is not specified then it is equal to $10$ and again as in the first case the bases are equal and $\log$ signs can be skipped:

## $5 m = 5125$

After dividing both sides by $5$ we get: