How do you evaluate $log_216 6$ ?

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Answer 1 · 2016-09-09T03:07:34

$log_(216)6=1/3$

A couple of things to know/remember to answer this:

$log_(216)6$ is asking how many times 216 needs to be multiplied by itself in order to arrive at 6. Clearly the answer is less than 1!

$216^(1/2)$ is the same as $sqrt216$ . $216^(1/3)$ is the same as $root(3)216$ . And so on.

Ok... what is $log_(216)6$ ?

One way to do this is to work from the 6 to the 216 - it turns out that:

$6^3=216$

Which means that

$216^(1/3)=6$

and so:

$log_(216)6=1/3$

How do you evaluate log_216 6log_216 6?