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

May 28, 2018

below

#### Explanation:

There are two ways of doing this question

(1) Using the change of base formula

${\log}_{a} b = {\log}_{10} \frac{b}{\log} _ 10 a$

${\log}_{5} \left(\frac{1}{25}\right) = {\log}_{10} \frac{\frac{1}{25}}{\log} _ 10 5 = - 2$

(2) Using the index law ${x}^{- n} = \frac{1}{x} ^ n$ and ${\log}_{a} a = 1$

${\log}_{5} \left(\frac{1}{25}\right) = {\log}_{5} \left({5}^{- 2}\right) = - 2$