Ratio, Proportion, Indices, LogarithmPYQ Dec. 21Question 939 of 305
All Questions

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
For any discrepancies in this question, email contact@cadada.in

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

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.

More Questions from Ratio, Proportion, Indices, Logarithm

3x−2:5x+6\displaystyle 3x-2:5x+6 the duplicate ratio of 2:3\displaystyle 2:3 then find the value x\displaystyle x.

If the ratio of two numbers is 7:11\displaystyle 7:11. If 7\displaystyle 7 is added to each number then the new ratio will be 2:3\displaystyle 2:3 then the numbers are.

If x:y=z:7=4:11\displaystyle x:y=z:7=4:11 then x+y+zz\displaystyle \frac{x+y+z}{z} is

The ratio of two numbers are 3:4\displaystyle 3:4. The difference of their squares is 28\displaystyle 28 greater is:

The price of scooter and moped are in the ratio 7:9\displaystyle 7:9. The price of moped is ₹1,600\displaystyle ₹1,600 more than that of scooter. Then the price of moped is:

If A:B=3:7\displaystyle A:B=3:7, then 3a+2b:4a+5b=?\displaystyle 3a+2b:4a+5b=?

Ready to Master Ratio, Proportion, Indices, Logarithm?

Practice all 305 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free