How do you evaluate ${log}_{216} 6$ $log_216 6$ ?

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How do you evaluate ${log}_{216} 6$ $log_216 6$ ?

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Answer 1 · 2016-09-09T03:07:34

${log}_{216} 6 = \frac{1}{3}$ $log_(216)6=1/3$

Explanation:

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

${log}_{216} 6$ $log_(216)6$ 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!

$216^{\frac{1}{2}}$ $216^(1/2)$ is the same as $\sqrt{216}$ $sqrt216$ . $216^{\frac{1}{3}}$ $216^(1/3)$ is the same as $\sqrt[3]{216}$ $root(3)216$ . And so on.

Ok... what is ${log}_{216} 6$ $log_(216)6$ ?

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

$6^{3} = 216$ $6^3=216$

Which means that

$216^{\frac{1}{3}} = 6$ $216^(1/3)=6$

and so:

${log}_{216} 6 = \frac{1}{3}$ $log_(216)6=1/3$

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How do you evaluate ${log}_{216} 6$ $log_216 6$ ?

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