Ratio, Proportion, Indices, LogarithmMCQPYQ June 22Question 941 of 305
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log⁡p2qr+log⁡q2pr+log⁡r2pq\displaystyle \log \frac{p^2}{qr} + \log \frac{q^2}{pr} + \log \frac{r^2}{pq} is:

Options

Apqr\displaystyle pqr
B0
C1
DNone of these
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Correct Answer

✅ Option b — 0

All Options:

  • Apqr\displaystyle pqr
  • B0
  • C1
  • DNone of these

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Detailed Solution & Explanation

Using the property log⁡A+log⁡B+log⁡C=log⁡(ABC)\displaystyle \log A + \log B + \log C = \log(ABC):

log⁡p2qr+log⁡q2pr+log⁡r2pq=log⁡(p2qr⋅q2pr⋅r2pq)\log \frac{p^2}{qr} + \log \frac{q^2}{pr} + \log \frac{r^2}{pq} = \log \left( \frac{p^2}{qr} \cdot \frac{q^2}{pr} \cdot \frac{r^2}{pq} \right)

Multiply the numerators and denominators:

=log⁡(p2⋅q2⋅r2qr⋅pr⋅pq)=log⁡(p2q2r2p2q2r2)= \log \left( \frac{p^2 \cdot q^2 \cdot r^2}{qr \cdot pr \cdot pq} \right) = \log \left( \frac{p^2 q^2 r^2}{p^2 q^2 r^2} \right)

=log⁡1=0= \log 1 = 0

**The answer is (b) 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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