How do you calculate log_5 7.2 with a calculator?

Aug 9, 2016

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:

${\log}_{a} \left(x\right) = \frac{{\log}_{10} x}{{\log}_{10} a}$

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

In our case we get:

${\log}_{5} \left(7.2\right) = \frac{{\log}_{10} \left(7.2\right)}{{\log}_{10} \left(5\right)} = 1.22656$