Ratio, Proportion, Indices, LogarithmMCQPYQ Dec. 21Question 939 of 305
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If log⁡103=x\displaystyle \log_{10} 3 = x and log⁡104=y\displaystyle \log_{10} 4 = y, then the value of log⁡10120\displaystyle \log_{10} 120 can be expressed as

Options

Ax−y+1\displaystyle x - y + 1
Bx+y+1\displaystyle x + y + 1
Cx+y−1\displaystyle x + y - 1
D2x+y+1\displaystyle 2x + y + 1
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Correct Answer

✅ Option b — x+y+1\displaystyle x + y + 1

All Options:

  • Ax−y+1\displaystyle x - y + 1
  • Bx+y+1\displaystyle x + y + 1
  • Cx+y−1\displaystyle x + y - 1
  • D2x+y+1\displaystyle 2x + y + 1

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Detailed Solution & Explanation

We are given:
log⁡103=x\log_{10} 3 = x
log⁡104=y\log_{10} 4 = y

We want to find the expression for log⁡10120\displaystyle \log_{10} 120. Let us factor the number 120\displaystyle 120 in terms of the given bases (3\displaystyle 3 and 4\displaystyle 4) and the logarithmic base (10\displaystyle 10):
120=3×4×10120 = 3 \times 4 \times 10

Now, apply the product rule of logarithms, log⁡b(A×B×C)=log⁡bA+log⁡bB+log⁡bC\displaystyle \log_b(A \times B \times C) = \log_b A + \log_b B + \log_b C:
log⁡10120=log⁡103+log⁡104+log⁡1010\log_{10} 120 = \log_{10} 3 + \log_{10} 4 + \log_{10} 10

We know that log⁡1010=1\displaystyle \log_{10} 10 = 1. Substitute the given values x\displaystyle x and y\displaystyle y into the equation:
log⁡10120=x+y+1\log_{10} 120 = x + y + 1

Hence, **Option B** is the correct answer.

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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