Given that log{10} 2 = x and log{10} 3 = y, the value of log{10} 120 is expressed as

Option b: 2x + y + 1. Solution: 120 = 2^2 x 3 x 10 = 4 x 30 log{10} 120 = log{10}(2^2 x 3 x 10) = 2log{10} 2 + log{10} 3 + log{10} 10 = 2x + y + 1 The answer is (b) 2x + y + 1.

Ratio, Proportion, Indices, LogarithmMTP Sep 24 Series IQuestion 981 of 305

All Questions

Given that $\displaystyle \log_{10} 2 = x$ and $\displaystyle \log_{10} 3 = y$ , the value of $\displaystyle \log_{10} 120$ is expressed as

Options

\displaystyle 2x - y + 1

\displaystyle 2x + y + 1

\displaystyle 2x - y - 1

DNone of these

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Correct Answer

✅ Option b — $\displaystyle 2x + y + 1$

All Options:

A $\displaystyle 2x - y + 1$
B $\displaystyle 2x + y + 1$
C $\displaystyle 2x - y - 1$
DNone of these

Detailed Solution & Explanation

120 = 2^2 \times 3 \times 10 = 4 \times 30

\log_{10} 120 = \log_{10}(2^2 \times 3 \times 10)

= 2\log_{10} 2 + \log_{10} 3 + \log_{10} 10

= 2x + y + 1

**The answer is (b)

\displaystyle 2x + y + 1

.**

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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Given that log⁡102=x\displaystyle \log_{10} 2 = xlog10​2=x and log⁡103=y\displaystyle \log_{10} 3 = ylog10​3=y, the value of log⁡10120\displaystyle \log_{10} 120log10​120 is expressed as