(D) Given that,$\log _{27}(\log _3 x) = \frac{1}{3}$.Using the definition of logarithm,$\log _a b = c \Rightarrow b = a^c$,we get:$\log _3 x = (27)^{1

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(D) Given that,$\log _{27}(\log _3 x) = \frac{1}{3}$.Using the definition of logarithm,$\log _a b = c \Rightarrow b = a^c$,we get:$\log _3 x = (27)^{1/3}$.Since $27 = 3^3$,we have $(27)^{1/3} = (3^3)^{1/3} = 3^1 = 3$.So,$\log _3 x = 3$.Again,using the definition of logarithm,$x = 3^3$.Therefore,$x = 27$.

Class 11 Mathematics Basic of Logarithms Logarithms

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If $\log _{27}(\log _3 x) = \frac{1}{3}$,then the value of $x$ is

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$3$
B
$6$
C
$9$
D
$27$

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