Question

How do you use the Change of Base Formula and a calculator to evaluate the logarithm `log_3 15`?

Answer 1

`log_3 15=ln15/ln3=log15/log3~~2.465`

Explanation:

The change of base formula allows you to change bases of logarithms:
`log_b a=lna/lnb=log_c a/log_c b` where `c` is the new base of your choice.
With `a=15` and `b=3`, we get that `log_3 15=ln15/ln3=log15/log3` (`logx` is the base 10 logarithm) and using a calculator, it is approximately 2.465. The reason why we normally use the natural logarithm or the base 10 logarithm is that most calculators are equipped with these functions.