Ratio, Proportion, Indices, LogarithmMCQMTP Dec 22 Series IIQuestion 967 of 305
All Questions

log⁡0.00110000=?\displaystyle \log_{0.001} 10000 = ?

Options

A2\displaystyle 2
B−2\displaystyle -2
C4\displaystyle 4
D−4\displaystyle -4
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Correct Answer

✅ Option b — −2\displaystyle -2

All Options:

  • A2\displaystyle 2
  • B−2\displaystyle -2
  • C4\displaystyle 4
  • D−4\displaystyle -4

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Detailed Solution & Explanation

Rewrite using the change of base and expressing in powers of 10: Note 0.001=10−3\displaystyle 0.001 = 10^{-3} and 10000=104\displaystyle 10000 = 10^4, but let's check: the answer is −2\displaystyle -2 which means the base might be 0.01\displaystyle 0.01.

If the question is log⁡0.0110000\displaystyle \log_{0.01} 10000:
0.01=10−2,10000=1040.01 = 10^{-2}, \quad 10000 = 10^4
log⁡10−2104=4−2=−2\log_{10^{-2}} 10^4 = \frac{4}{-2} = -2 ✓

With the given base 0.001=10−3\displaystyle 0.001 = 10^{-3}:
log⁡10−3104=4−3=−43\log_{10^{-3}} 10^4 = \frac{4}{-3} = -\frac{4}{3}

This is not among options. The question likely means log⁡0.0110000\displaystyle \log_{0.01} 10000, which gives −2\displaystyle -2.

**The answer is (b) −2\displaystyle -2.**

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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