If logx(916)=−12, then the value of x

logx916=−12916=x−12916=1xx=169x=25681

If logx(916)=−12, then the value of x

logx916=−12916=x−12916=1xx=169x=25681

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If $\log_{x} (\frac{9}{16}) = \frac{- 1}{2}$ , then the value of $x$

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$\frac{3}{4}$

$\frac{256}{81}$

$\frac{81}{216}$

$\frac{- 3}{4}$

answer is D.

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Detailed Solution

$\log_{x} (\frac{9}{16}) = \frac{- 1}{2}$

$\frac{9}{16} = x^{\frac{- 1}{2}}$

$\frac{9}{16} = \frac{1}{\sqrt{x}}$

$\sqrt{x} = \frac{16}{9}$

$x = \frac{256}{81}$

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If $\log_{x} (\frac{9}{16}) = \frac{- 1}{2}$ , then the value of $x$