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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2011 · Mathematics · Basics of Mathematics

What is the value of _2( _3 81) ?

What is the value of log⁡2(log⁡381)?\log _2\left(\log _3 81\right) ?

Options

  1. A22
  2. B33
  3. C44
  4. D99

Correct answer

A. 22

Step-by-step solution

 Let, log⁡381=x⇒3x=81=(3)4⇒x=4and let log⁡24=y⇒(2)y=4=(2)2⇒y=2∴log⁡2(log⁡381)=2\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}$$
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