How do you evaluate log_6(216)?

1 Answer
mason m
Nov 16, 2015

If log_6(216)=x, we can say that x=log_6(6^3)=3log_6(6)=3.

Basically, if you have a logarithm log_a(b), you can ask yourself, "a to WHAT power gives me b?"

In this situation, 6 to the 3rd power will give you 216, so the answer is 3.

In situations where the answer won't be an easy integer or fraction, you can input a logarithm in the form log_a(b) in your calculator simply as logb/loga in your calculator. You can put log216/log6 into your calculator and it will spit out an answer of 3.

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