What is x if ${log}_{4} (16 x) = \frac{1}{2}$ $log_4(16x) = 1/2$ ?

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Answer 1 · 2015-10-22T23:06:14

$\frac{1}{8}$ $1/8$

According to the definition of logarithm ${log}_{4} (16 x) = \frac{1}{2}$ $log_4(16x)=1/2$ is equal to $4^{\frac{1}{2}}$ $4^(1/2)$ = $16 x$ $16x$

$4^{\frac{1}{2}} = 2$ $4^(1/2)=2$ so you have $2 = 16 x$ $2=16x$

Divide both sides by 16, which gives you
$\frac{2}{16} = x$ $2/16=x$ or $x = \frac{1}{8}$ $x=1/8$

What is x if log4(16x)=12log_4(16x) = 1/2?