How do you evaluate $log_64 (1/2)$ ?

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Answer 1 · 2016-09-12T07:46:46

$-1/6$

Recall that $log_2(8)=3, => 2^3=8$

let $log_64(1/2)=x$

$64^x=1/2$

$64=2^6$
$64^x=2^(6x)$
$1/2=2^-1$

$2^(6x)=2^-1$
$6x=-1$
$x=-1/6$

How do you evaluate log_64 (1/2)log_64 (1/2)?