How do you evaluate $log_216 6$ ?

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Answer 1 · 2016-08-29T20:55:06

$1/3$

$6^2 = 36$

$6^3 = 36 * 6 = 180+36 = 216$

So $216^(1/3) = 6$

and $log_216 6 = 1/3$

Answer 2 · 2016-08-29T20:55:24

$log_216 6 = 1/3$

By the $log$ rule $log_a(n) = (logn)/(loga)$ :

$log_216(6) = (log6)/(log216) = (log(6^1))/(log(6^3))$

Now use the rule $log(a^n) = nloga$ and simplify:

$=(1log6)/(3log6)$

$=1/3$

How do you evaluate log_216 6log_216 6?