Ratio, Proportion, Indices, LogarithmMCQMTP Sep 24 Series IIQuestion 982 of 302
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log⁡a2bc+log⁡b2ca+log⁡c2ab=\displaystyle \log \frac{a^2}{bc} + \log \frac{b^2}{ca} + \log \frac{c^2}{ab} =

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 0\displaystyle 0

All Options:

  • A0\displaystyle 0
  • B1\displaystyle 1
  • Clog⁡a\displaystyle \log a
  • DNone of these

Detailed Solution & Explanation

Using the product rule of logarithms:

log⁡a2bc+log⁡b2ca+log⁡c2ab=log⁡(a2bc⋅b2ca⋅c2ab)\log a2bc+log⁡\displaystyle \frac{a^2}{bc} + \log b2ca+log⁡\displaystyle \frac{b^2}{ca} + \log c2ab=log⁡\displaystyle \frac{c^2}{ab} = \log\left(a2bc\displaystyle \frac{a^2}{bc} ⋅\displaystyle \cdot b2ca\displaystyle \frac{b^2}{ca} ⋅\displaystyle \cdot c2ab\displaystyle \frac{c^2}{ab}\right)

Multiply numerators: a2⋅b2⋅c2=a2b2c2\displaystyle a^2 ⋅\displaystyle \cdot b^2 ⋅\displaystyle \cdot c^2 = a^2 b^2 c^2

Multiply denominators: bc⋅ca⋅ab=a2b2c2\displaystyle bc ⋅\displaystyle \cdot ca ⋅\displaystyle \cdot ab = a^2 b^2 c^2

=log⁡(a2b2c2a2b2c2)=log⁡1=0= \log\left(a2b2c2a2b2c2\displaystyle \frac{a^2 b^2 c^2}{a^2 b^2 c^2}\right) = \log 1 = 0

**The answer is (a) 0.**

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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