Given that logx 2 = x and logx 3 = y , the value of logx 60 is expressed as

Option b: x + y + 1. Solution: We are given loga 2 = x and loga 3 = y (using base a consistently). loga 60 = loga (22 × 3 × 5) But this introduces loga 5 . Instead: 60 = 6 × 10 = 2 × 3 × 10 If the base is 10: log10 60 = log10(2 × 3 × 10) = log10 2 + log10 3 + log10 10 = x + y + 1 The answer is (b) x + y + 1 .

Given that $\log_x 2 = x$ and $\log_x 3 = y$, the value of $\log_x 60$ is expressed as

The correct answer is Option b: $x + y + 1$. We are given $\log_a 2 = x$ and $\log_a 3 = y$ (using base $a$ consistently). $$\log_a 60 = \log_a (2^2 \times 3 \times 5)$$ But this introduces $\log_a 5$. Instead: $$60 = 6 \times 10 = 2 \times 3 \times 10$$ If the base is 10: $$\log_{10} 60 = \log_{10}(2 \times 3 \times 10) = \log_{10} 2 + \log_{10} 3 + \log_{10} 10$$ $$= x + y + 1$$ **The answer is (b) $x + y + 1$.**

Ratio, Proportion, Indices, LogarithmMCQMTP May 20Question 957 of 305

All Questions

Given that $\displaystyle \log_x 2 = x$ and $\displaystyle \log_x 3 = y$ , the value of $\displaystyle \log_x 60$ is expressed as

Options

\displaystyle x - y + 1

\displaystyle x + y + 1

\displaystyle x - y - 1

Dnone of these

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Correct Answer

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

All Options:

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

Detailed Solution & Explanation

We are given

\displaystyle \log_a 2 = x

and

\displaystyle \log_a 3 = y

(using base

\displaystyle a

consistently).

\log_a 60 = \log_a (2^2 \times 3 \times 5)

But this introduces

\displaystyle \log_a 5

. Instead:

60 = 6 \times 10 = 2 \times 3 \times 10

If the base is 10:

\log_{10} 60 = \log_{10}(2 \times 3 \times 10) = \log_{10} 2 + \log_{10} 3 + \log_{10} 10

= x + y + 1

**The answer is (b)

\displaystyle x + 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⁡x2=x\displaystyle \log_x 2 = xlogx​2=x and log⁡x3=y\displaystyle \log_x 3 = ylogx​3=y, the value of log⁡x60\displaystyle \log_x 60logx​60 is expressed as