CAT Logarithms Questions & Solutions

A sample of real CAT Logarithms past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 54 Logarithms questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   The number of distinct integers $n$ for which $\log_{\frac{1}{4}}({n^{2}-7n+11})>0$,is

   • 2

   • infinite

   • 1

   • 0

2. Q2.CAT 2024

   If $(x + 6\sqrt{2})^{\cfrac{1}{2}} - (x - 6\sqrt{2})^{\cfrac{1}{2}} = 2\sqrt{2}$, then x equals

   Answer: 11

3. Q3.CAT 2024

   If $3^a = 4, 4^b = 5, 5^c = 6, 6^d = 7, 7^e = 8$ and $8^f = 9$, then the value of the product abcdef is

   Answer: 2

4. Q4.CAT 2023

   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

   Answer: 7

5. Q5.CAT 2020

   If Y is a negative number such that $2^{Y^2({\log_{3}{5})}}=5^{\log_{2}{3}}$, then Y equals to:

   • $\log_{2}(\frac{1}{5})$

   • $\log_{2}(\frac{1}{3})$

   • $-\log_{2}(\frac{1}{5})$

   • $-\log_{2}(\frac{1}{3})$

6. Q6.CAT 2020

   If a,b,c are non-zero and $14^a=36^b=84^c$, then $6b(\frac{1}{c}-\frac{1}{a})$ is equal to

   Answer: 3

7. Q7.CAT 2019

   If m and n are integers such that $(\surd2)^{19} 3^4 4^2 9^m 8^n = 3^n 16^m (\sqrt[4]{64})$ then m is

   • -20

   • -24

   • -12

   • -16

8. Q8.CAT 2018

   Given that $x^{2018}y^{2017}=\frac{1}{2}$, and $x^{2016}y^{2019}=8$, then value of $x^{2}+y^{3}$ is

   • $\dfrac{31}{4}$

   • $\dfrac{35}{4}$

   • $\dfrac{37}{4}$

   • $\dfrac{33}{4}$

9. Q9.CAT 2017

   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

   • $\sqrt{a}$

   • 2a

   • a/2

   • a

10. Q10.CAT 2017

    If $9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$, then $x$ is
    

    • $\frac{3}{2}$

    • $\frac{2}{5}$

    • $\frac{3}{4}$

    • $\frac{4}{9}$

11. Q11.CAT 2006

    If $log_y x = (a*log_z y) = (b*log_x z) = ab$, then which of the following pairs of values for (a, b) is not possible?

    • (-2, $\frac{1}{2}$)

    • (1,1)

    • (0.4, 2.5)

    • ($\pi$, 1/ $\pi$)

    • (2,2)

12. Q12.CAT 2002

    If $f(x) = \log \frac{(1+x)}{(1-x)}$, then f(x) + f(y) is

    • $f(x+y)$

    • $f{\frac{(x+y)}{(1+xy)}}$

    • $(x+y)f{\frac{1}{(1+xy)}}$

    • $\frac{f(x)+f(y)}{(1+xy)}$

CAT Logarithms previous year questions with solutions — AthenaPrep