ABC26GN1979 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
If $2^{x}=4^{y}=8^{z}$ and $\left(\frac{1}{2 x}+\frac{1}{4 y}+\frac{1}{6 z}\right)=\frac{24}{7}$, then the value of $z$ is
(a)$\frac{7}{16}$
(b)$\frac{7}{32}$
(c)$\frac{7}{48}$
(d)$\frac{7}{64}$
Answer
Explanation
$2^{x}=4^{y}=8^{z} \Leftrightarrow 2^{x}=2^{2 y}=2^{3 z} \Leftrightarrow x=2 y=3 z$. $$\begin{aligned} \therefore \quad \frac{1}{2 x}+\frac{1}{4 y}+\frac{1}{6 z}=\frac{24}{7} & \Leftrightarrow \frac{1}{6 z}+\frac{1}{6 z}+\frac{1}{6 z}=\frac{24}{7} \\ & \Leftrightarrow \frac{3}{6 z}=\frac{24}{7} \Leftrightarrow z=\left(\frac{3}{6} \times \frac{7}{24}\right)=\frac{7}{48} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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