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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2016 · Mathematics · Basics of Mathematics

If _a(a b)=x , then what is _b(a b) equal to?

If log⁡a(ab)=x\log _a(a b)=x, then what is log⁡b(ab)\log _b(a b) equal to?

Options

  1. A1x\frac{1}{x}
  2. Bxx+1\frac{x}{x+1}
  3. Cx1−x\frac{x}{1-x}
  4. Dxx−1\frac{x}{x-1}

Correct answer

D. xx−1\frac{x}{x-1}

Step-by-step solution

log⁡aab=xlog⁡aa+log⁡ab=x1log⁡ba=x−1\begin{aligned} & \log _a a b=x \\ & \log _a a+\log _a b=x \\ & \frac{1}{\log _b a}=x-1\end{aligned}log⁡ba=1x−1...(i)log⁡bab=log⁡ba+log⁡bb=1x−1+1(From(1))=1+x−1x−1log⁡bab=xx−1\begin{aligned} \log _b a & =\frac{1}{x-1}...(i) \\ \log _b a b & =\log _b a+\log _b b \\ & =\frac{1}{x-1}+1 \quad(From (1))\\ & =\frac{1+x-1}{x-1} \\ \log _b a b & =\frac{x}{x-1}\end{aligned}$
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