Question

How do you calculate `log_5 7.2` with a calculator?

Answer 1

I found: `1.22656`

Explanation:

Normally in a calculator you have two types of logs: one in base `e` and the other in base `10`.
Our log is in base `5` but it isn't a problem because we can change base using the relationship:

`log_a(x)=(log_(10)x)/(log_(10)a)`

where we used the new base `10` that can be evaluated.

In our case we get:

`log_5(7.2)=(log_(10)(7.2))/(log_(10)(5))=1.22656`