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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2015 · Mathematics · Basics of Mathematics

If _8 m+ _8 (1)/(6)=(2)/(3) , then m is equal to

If log⁡8m+log⁡816=23\log _8 \mathrm{ m}+\log _8 \frac{1}{6}=\frac{2}{3}, then m is equal to

Options

  1. A24
  2. B18
  3. C12
  4. D4

Correct answer

A. 24

Step-by-step solution

log⁡8m+log⁡816=23⇒log⁡8(m⋅16)=23⇒(8)23=m⋅16⇒m=24\begin{aligned} & \log _8 \mathrm{ m}+\log _8 \frac{1}{6}=\frac{2}{3} \\ & \Rightarrow \quad \log _8\left(\mathrm{ m} \cdot \frac{1}{6}\right)=\frac{2}{3} \\ & \Rightarrow \quad(8)^{\frac{2}{3}}=\mathrm{m} \cdot \frac{1}{6} \\ & \Rightarrow \mathrm{ m}=24\end{aligned}
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