Question

How do you use the Change of Base Formula and a calculator to evaluate the logarithm `log_5 (1/25)`?

Answer 1

below

Explanation:

There are two ways of doing this question

(1) Using the change of base formula

`log_ab = log_10b/log_10a`

`log_5(1/25) = log_10(1/25)/log_10 5 = -2`

(2) Using the index law `x^(-n) = 1/x^n` and `log_a a=1`

`log_5(1/25) = log_5(5^(-2)) = -2`