How do you simplify ${log}_{2} 8$ $log_2 8$ ?

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Answer 1 · 2016-05-23T15:09:29

First use the change of base rule ${log}_{n} a = \frac{log a}{log n}$ $log_na = loga/logn$

$= \frac{log 8}{log 2}$ $= log8/log2$

$= \frac{log (2^{3})}{log 2}$ $= log(2^3)/log2$

By the rule ${log n}^{a} = a log n$ $logn^a = alogn$

$= \frac{3 log 2}{log 2}$ $=(3log2)/log2$

$= 3$ $= 3$

Hopefully this helps.

How do you simplify log28log_2 8?