Ratio, Proportion, Indices, LogarithmMCQPYQ Nov. 20Question 935 of 305

If $\displaystyle \log_x \sqrt{3} = \frac{1}{6}$ find the value of $\displaystyle a$ :

B81

C27

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

Correct Answer

✅ Option c — 27

We are given the logarithmic equation:

\log_x \sqrt{3} = \frac{1}{6}

Let us write this equation in its equivalent exponential form:

x^{1/6} = \sqrt{3}

We know that

\displaystyle \sqrt{3} = 3^{1/2}

. Substituting this into the equation:

x^{1/6} = 3^{1/2}

To solve for

\displaystyle x

(referred to as

\displaystyle a

in the textbook typo), let us raise both sides of the equation to the power of

\displaystyle 6

\left( x^{1/6} \right)^6 = \left( 3^{1/2} \right)^6

x = 3^{6/2}

x = 3^3 = 27

Hence, **Option C** is the correct answer.

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.

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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