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How do you solve for x in $2^{log x} = \frac{1}{4}$ $2^ logx = 1/4$ ?

1 Answer

Dec 22, 2015

$x = 0.01$ $x=0.01$

Explanation:

Note that
$XXX \frac{1}{4} = \frac{1}{2^{2}} = 2^{- 2}$ $color(white)("XXX")1/4=1/(2^2)=2^(-2)$

So if $2^{log (x)} = \frac{1}{4}$ $2^(log(x)) = 1/4$
then
$XXX log (x) = - 2$ $color(white)("XXX")log(x)=-2$

$XXX 10^{- 2} = x$ $color(white)("XXX")10^(-2) = x$ (based on definition of log)

$XXX x = \frac{1}{100} = 0.01$ $color(white)("XXX")x=1/100 = 0.01$

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