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

Question

1757 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-28T11:20:40

below

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 $log_a a=1$

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

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