How to use the Change of Base Formula and a calculator to evaluate the logarithm log_3 15?

Ainsley Boyle

Ainsley Boyle

Answered question

2023-01-19

How to use the Change of Base Formula and a calculator to evaluate the logarithm log315?

Answer & Explanation

michellegrosscju

michellegrosscju

Beginner2023-01-20Added 9 answers

You can switch the bases of logarithms using the change of base formula:
logba=lnalnb=logcalogcb where c is the new base of your choice.
With a=15 and b=3, we get that log315=ln15ln3=log15log3 (logx is the base 10 logarithm) and using a calculator, it is approximately 2.465. The reason why we normally use the natural logarithm or the base 10 logarithm is that most calculators are equipped with these functions.

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