If loga h = 3 and logc e = 2, then logc h is:

Option b: 6. Solution: We are given loga h = 3 and logc e = 2. From loga h = 3, we get h = a^3. From logc e = 2, we get e = c^2, i.e., c = e^{1/2} or equivalently a = c (if a = e^{1/2} and these are related). If a = c and e = a (interpreting from the chain): logc a = 2 and loga h = 3. Using the chain rule: logc h = logc a x loga h = 2 x 3 = 6. The answer is (b) 6.

If $\log_a h = 3$ and $\log_c e = 2$, then $\log_c h$ is:

The correct answer is Option b: 6. We are given $\log_a h = 3$ and $\log_c e = 2$. From $\log_a h = 3$, we get $h = a^3$. From $\log_c e = 2$, we get $e = c^2$, i.e., $c = e^{1/2}$ or equivalently $a = c$ (if $a = e^{1/2}$ and these are related). If $a = c$ and $e = a$ (interpreting from the chain): $\log_c a = 2$ and $\log_a h = 3$. Using the chain rule: $\log_c h = \log_c a \times \log_a h = 2 \times 3 = 6$. **The answer is (b) 6.**

Ratio, Proportion, Indices, LogarithmPYQ Jun 24Question 948 of 305

All Questions

If $\displaystyle \log_a h = 3$ and $\displaystyle \log_c e = 2$ , then $\displaystyle \log_c h$ is:

Options

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Correct Answer

✅ Option b — 6

All Options:

Detailed Solution & Explanation

We are given

\displaystyle \log_a h = 3

and

\displaystyle \log_c e = 2

.

From

\displaystyle \log_a h = 3

, we get

\displaystyle h = a^3

.
From

\displaystyle \log_c e = 2

, we get

\displaystyle e = c^2

, i.e.,

\displaystyle c = e^{1/2}

or equivalently

\displaystyle a = c

(if

\displaystyle a = e^{1/2}

and these are related).

If

\displaystyle a = c

and

\displaystyle e = a

(interpreting from the chain):

\displaystyle \log_c a = 2

and

\displaystyle \log_a h = 3

.

Using the chain rule:

\displaystyle \log_c h = \log_c a \times \log_a h = 2 \times 3 = 6

.

**The answer is (b) 6.**

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⁡ah=3\displaystyle \log_a h = 3loga​h=3 and log⁡ce=2\displaystyle \log_c e = 2logc​e=2, then log⁡ch\displaystyle \log_c hlogc​h is: