How do you use the Change of Base Formula and a calculator to evaluate the logarithm ${log}_{5} (\frac{1}{25})$ $log_5 (1/25)$ ?

Question

1720 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

${log}_{a} b = \frac{{log}_{10} b}{{log}_{10} a}$ $log_ab = log_10b/log_10a$

${log}_{5} (\frac{1}{25}) = \frac{{log}_{10} (\frac{1}{25})}{{log}_{10} 5} = - 2$ $log_5(1/25) = log_10(1/25)/log_10 5 = -2$

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

${log}_{5} (\frac{1}{25}) = {log}_{5} (5^{- 2}) = - 2$ $log_5(1/25) = log_5(5^(-2)) = -2$

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_5 (1/25)log5(125)log_5 (1/25)?