How do you express #3log_5 4 - 5log_5 2# as a single logarithm?
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:
So, our expression becomes:
There could be other answers using different bases.