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

1 Answer
Lucy
May 28, 2018

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#

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