How do you evaluate #log_6(216)#?

1 Answer
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#.