The CAT QA section requires speed and accuracy, along with a thorough understanding of the Logarithms. This article provides a set of MCQs on Logarithms to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Logarithms
1. If \(x\) and \(y\) are positive real numbers such that \(log_x(x^2+12)=4\) and \(3\;log_yx=1\),then \(x+y\) equals
A
11
B
20
C
10
D
68
2. For some positive real number \(x\) , if \(log_{\sqrt 3}(x)+\frac{log_x(25)}{log_x(0.008)}=\frac{16}{3}\), then the value of \(log_3(3x^2)\) is
A
4
B
6
C
7
D
9
3. For a real number \(x\) , if \(\frac{1}{2},\frac{log_3(2^x-9)}{log_34}\), and \(\frac{log_5\bigg(2^x+\frac{17}{2}\bigg)}{log_54}\) are in an arithmetic progression, then the common difference is
A
\(log_4\bigg(\frac{23}{2}\bigg)\)
B
\(log_4\bigg(\frac{3}{2}\bigg)\)
C
\(log_47\)
D
\(log_4\bigg(\frac{7}{2}\bigg)\)
4. If \(y\) is a negative number such that \(2^{y^2log_35 }\)= \(5^{log_23}\), then \(y\) equals
A
\(log_2 \bigg(\frac{1}{3}\bigg)\)
B
\(-log \bigg(\frac{1}{3}\bigg)\)
C
\(log \bigg(\frac{1}{5}\bigg)\)
D
\(-log \bigg(\frac{1}{5}\bigg)\)
5. The value of \( \log_a\left(\frac{a}{b}\right) + \log_b\left(\frac{b}{a}\right) \), for \( 1 < a \leq b \) cannot be equal to
A
-0.5
B
1
C
0
D
-1
6. If \(log_a\) \(30\) = \(A\), \(log_a\) \(\bigg(\frac{5}{3}\bigg)\) = \(-B\) and \(log_2\; a\) = \(\frac{1}{3}\), then \(log_3\) \(a\) equals.
A
\(\frac{2}{A+B}-3\)
B
\(\frac{A+B-3}{2}\)
C
\(\frac{2}{A+B-3}\)
D
\(\frac{A+B}{2}-3\)
7. If \(log_45=(log_4y)(log_6\sqrt5)\),then \(y\) equals
[This Question was asked as TITA]
[This Question was asked as TITA]
A
34
B
36
C
38
D
37
8. \(\frac{2×4×8×16}{(log_24)^2(log_48)^3(log_816)^4}\) equals [This Question was asked as TITA]
A
25
B
24
C
22
D
23
9. Let x and y be positive real numbers such that log5(x+y) + log5(x-y) = 3, and log2y - log2x = 1 - log23. Then xy equals
A
250
B
25
C
100
D
150
10. Suppose, \(log_3 \ x = log_{12} \ y = a\), where x, y are positive numbers. If G is the geometric mean of x and y, and \(log_6\) G is equal to
A
\(\sqrt{a}\)
B
2a
C
\(\frac{a}{2}\)
D
a
11. The value of \(\text {log}_{0.008}\sqrt{5}+\text{log}_{\sqrt{3}}81-7\) is equal to
A
\(\frac{1}{3}\)
B
\(\frac{2}{3}\)
C
\(\frac{5}{6}\)
D
\(\frac{7}{6}\)
12. If x is a real number such that log3 5 = log5 (2 + x), then which of the following is true?
A
0 < x < 3
B
23 < x < 30
C
x > 30
D
3 < x < 23
13. If log (2a × 3b × 5C) is the arithmetic mean of log (22 × 33 × 5), log (26 × 3 × 57 ), and log (2 × 32 × 54 ), then a equals
A
4
B
5
C
3
D
2
14. If log 2(5+log3a)=3 and log5(4a+12+log2b) = 3, then a+b is equal to
A
67
B
40
C
32
D
59
15. If x is a positive quantity such that 2x = 3log52, then x is equal to
A
1+log35/3
B
log58
C
1+log53/5
D
log59
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