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If $\log _{27}\left(\log _3 x\right)=\frac{1}{3}$, then the value of $x$ is
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Verified Answer
The correct answer is:
$27$
Given that,
$\begin{aligned}
& & \log _{27}\left(\log _3 x\right) & =\frac{1}{3} \\
\Rightarrow & & \left(\log _3 x\right) & =(27)^{1 / 3} \quad\left[\because \log _a x=b \Rightarrow x=a^b\right] \\
\Rightarrow & & \log _3 x & =3 \\
& \therefore & x & =(3)^3 \Rightarrow x=27
\end{aligned}$
$\begin{aligned}
& & \log _{27}\left(\log _3 x\right) & =\frac{1}{3} \\
\Rightarrow & & \left(\log _3 x\right) & =(27)^{1 / 3} \quad\left[\because \log _a x=b \Rightarrow x=a^b\right] \\
\Rightarrow & & \log _3 x & =3 \\
& \therefore & x & =(3)^3 \Rightarrow x=27
\end{aligned}$
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