# How do you express #3log_5 4 - 5log_5 2# as a single logarithm?

##### 1 Answer

Apr 8, 2017

#### Explanation:

To solve this, you will need to use the "Change of Base" formula:

where we change the base-

Let's see how we can apply this to what we have.

I notice that we have a 4 and a 2 inside a base-5 logarithm.

So maybe I should change to a base-2 logarithm.

Let's see how each log transforms:

but since

so

and similarly,

So, our expression becomes:

i.e.

There could be other answers using different bases.