Question

How do you evaluate `log_6(216)`?

Answer 1

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`.