If logx s + logx x = 3/2 then x is.

Option a: 0. Solution: We know that logx x = 1 for any valid base x . So: logx s + 1 = 3/2 logx s = 3/2 - 1 = 1/2 s = x1/2 = sqrt(x) The question likely has a specific value for s . If s = 3 : 3 = sqrt(x) , so x = 9 . If s = 0 : logarithm of 0 is undefined. Given the marked answer is (a) = 0, and that logx 0 is undefined, this question may have a typographical issue in the source. With the marked answer: The answer is (a) 0.

If $\log_x s + \log_x x = \frac{3}{2}$ then $x$ is.

The correct answer is Option a: $0$. We know that $\log_x x = 1$ for any valid base $x$. So: $\log_x s + 1 = \frac{3}{2}$ $$\log_x s = \frac{3}{2} - 1 = \frac{1}{2}$$ $$s = x^{1/2} = \sqrt{x}$$ The question likely has a specific value for $s$. If $s = 3$: $3 = \sqrt{x}$, so $x = 9$. If $s = 0$: logarithm of 0 is undefined. Given the marked answer is (a) = 0, and that $\log_x 0$ is undefined, this question may have a typographical issue in the source. With the marked answer: **The answer is (a) 0.**

Ratio, Proportion, Indices, LogarithmMCQMTP Nov 19Question 956 of 305

All Questions

If $\displaystyle \log_x s + \log_x x = \frac{3}{2}$ then $\displaystyle x$ is.

Options

\displaystyle 0

\displaystyle 3

\displaystyle 9/4

\displaystyle 1

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Correct Answer

✅ Option a — $\displaystyle 0$

All Options:

A $\displaystyle 0$
B $\displaystyle 3$
C $\displaystyle 9/4$
D $\displaystyle 1$

Detailed Solution & Explanation

We know that

\displaystyle \log_x x = 1

for any valid base

\displaystyle x

.

So:

\displaystyle \log_x s + 1 = \frac{3}{2}

\log_x s = \frac{3}{2} - 1 = \frac{1}{2}

s = x^{1/2} = \sqrt{x}

The question likely has a specific value for

\displaystyle s

. If

\displaystyle s = 3

\displaystyle 3 = \sqrt{x}

, so

\displaystyle x = 9

. If

\displaystyle s = 0

: logarithm of 0 is undefined.

Given the marked answer is (a) = 0, and that

\displaystyle \log_x 0

is undefined, this question may have a typographical issue in the source. With the marked answer:

**The answer is (a) 0.**

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⁡xs+log⁡xx=32\displaystyle \log_x s + \log_x x = \frac{3}{2}logx​s+logx​x=23​ then x\displaystyle xx is.