How do you evaluate $log_16 (1/2)$ ?

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Answer 1 · 2018-05-03T21:41:05

$-1/4$

$log_16(1/2) = x$

We know that $log_b(x) = y$ equals to $b^y = x$ . Therefore, we can rewrite it as:
$16^x = 1/2$

Make both sides have a base of $2$ :
$2^(4x) = 2^-1$

Since both sides have the same base, it becomes:
$4x = -1$

Divide both sides by $color(blue)4$ :
$(4x)/color(blue)4 = -1/color(blue)4$

Therefore,
$x = -1/4$

The answer is $-1/4$ .

Hope this helps!

How do you evaluate log_16 (1/2)log_16 (1/2)?