If log x (9/16)=-1/2, then x is equal to · ABC26GN2025
Subject: General Aptitude · Chapter: Logarithms
If $\log _{x}\left(\frac{9}{16}\right)=-\frac{1}{2}$, then $x$ is equal to
(a)$-\frac{3}{4}$
(b)$\frac{3}{4}$
(c)$\frac{81}{256}$
(d)$\frac{256}{81}$
Answer
Explanation
$\log _{x}\left(\frac{9}{16}\right)=-\frac{1}{2} \Leftrightarrow x^{-1 / 2}=\frac{9}{16} \Leftrightarrow \frac{1}{\sqrt{x}}=\frac{9}{16} \Leftrightarrow \sqrt{x}=\frac{16}{9}$ $\Leftrightarrow x=\left(\frac{16}{9}\right)^{2}=\frac{256}{81}$.
Explanation as extracted from the printed page; notation may be imperfect.
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