If log10 2 = y and log10 3 = x , then the value of log10 15 is:

Option a: x - y + 1. Solution: We need log10 15 . log10 15 = log10 30/2 = log10 30 - log10 2 = log10(3 × 10) - log10 2 = log10 3 + log10 10 - log10 2 = x + 1 - y = x - y + 1 The answer is (a) x - y + 1 .

Ratio, Proportion, Indices, LogarithmMCQPYQ Dec. 22Question 944 of 305

All Questions

If $\displaystyle \log_{10} 2 = y$ and $\displaystyle \log_{10} 3 = x$ , then the value of $\displaystyle \log_{10} 15$ is:

Options

\displaystyle x - y + 1

\displaystyle x + y + 1

\displaystyle x + y - 1

\displaystyle x - y - 1

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Correct Answer

✅ Option a — $\displaystyle x - y + 1$

All Options:

A $\displaystyle x - y + 1$
B $\displaystyle x + y + 1$
C $\displaystyle x + y - 1$
D $\displaystyle x - y - 1$

Detailed Solution & Explanation

We need

\displaystyle \log_{10} 15

\log_{10} 15 = \log_{10} \frac{30}{2} = \log_{10} 30 - \log_{10} 2

= \log_{10}(3 \times 10) - \log_{10} 2

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

= x + 1 - y

= x - y + 1

**The answer is (a)

\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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If log⁡102=y\displaystyle \log_{10} 2 = ylog10​2=y and log⁡103=x\displaystyle \log_{10} 3 = xlog10​3=x, then the value of log⁡1015\displaystyle \log_{10} 15log10​15 is: