Q252 / 270 · NDA 2011 (Phase 2) · Mathematics

What is the value of $\log _2\left(\log _3 81\right) ?$

  • Correct answer
    A
    $2$
  • B
    $3$
  • C
    $4$
  • D
    $9$

Solution

$\begin{aligned} & \text { Let, } \log _3{ }^{81}=x \Rightarrow 3^x=81=(3)^4 \Rightarrow x=4 \\ & \text {and let } \log _2{ }^4=y \Rightarrow(2)^y=4=(2)^2 \Rightarrow y=2 \\ & \therefore \log _2\left(\log _3{ }^{81}\right)=2\end{aligned}$

Hence, the correct answer is option: 'A'.

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