Top CAT Quant Logarithms Questions [Download PDF]

Naveen Neredimalli

132

Jun 03, 2024

Top CAT Quant Logarithms Questions [Download PDF]

Logarithms are a key topic in the CAT Quantitative Ability (QA) section and have consistently appeared in CAT exams over the years. The questions on logarithms are usually straightforward, so students should not ignore this topic. Typically, the new format of the CAT Quant section includes 1-2 questions on logarithms. It is essential to understand the basics of logarithms well and practice related questions. 

Also, do check out all the Logarithms questions for CAT from the CAT previous year papers with detailed video solutions. This article will look into some important questions for the CAT logarithms. Take 3 Free CAT Mock Tests which will help you know where you currently stand, and will help you in analysing your strengths and weaknesses. These questions are usually straightforward, making it crucial for students not to overlook this topic. It is advisable to master the basics of CAT Logarithms and practice related questions. Additionally, check o CAT past papers for Logarithms questions with detailed video solutions in PDF format.

Question 1

If $$log_3 2, log_3 (2^x - 5), log_3 (2^x - 7/2)$$ are in arithmetic progression, then the value of x is equal to


Question 2

Let $$u = ({\log_2 x})^2 - 6 {\log_2 x} + 12$$ where x is a real number. Then the equation $$x^u = 256$$, has


Question 3

If x = -0.5, then which of the following has the smallest value?


Question 4

Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?


Question 5

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?


Question 6

If x >= y and y > 1, then the value of the expression $$log_x (x/y) + log_y (y/x)$$ can never be


Question 7

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

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Question 8

$$2^{73}-2^{72}-2^{71}$$ is the same as


Question 9

Find the value of $$\frac{1}{1 + \frac{1}{3-\frac{4}{2+\frac{1}{3-\frac{1}{2}}}}}$$ + $$\frac{3}{3 - \frac{4}{3+\frac{1}{2-\frac{1}{2}}}}$$

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Question 10

If $$\log_{2}{\log_{7}{(x^2 - x+37)}}$$ = 1, then what could be the value of ‘x’?


Question 11

Which of the following is true?

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Question 12

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


Question 13

The value of $$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$ is equal to


Question 14

If $$9^{2x-1}-81^{x-1}=1944$$, then $$x$$ is


Question 15

If x is a real number such that $$\log_{3}5= \log_{5}(2 + x)$$, then which of the following is true?


Question 16

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


Question 17

If $$log(2^{a}\times3^{b}\times5^{c} )$$is the arithmetic mean of $$log ( 2^{2}\times3^{3}\times5)$$, $$log(2^{6}\times3\times5^{7} )$$, and $$log(2 \times3^{2}\times5^{4} )$$, then a equals


Question 18

If x is a positive quantity such that $$2^{x}=3^{\log_{5}{2}}$$. then x is equal to


Question 19

If $$\log_{12}{81}=p$$, then $$3(\dfrac{4-p}{4+p})$$ is equal to


Question 20

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


Question 21

If $$\log_{2}({5+\log_{3}{a}})=3$$ and $$\log_{5}({4a+12+\log_{2}{b}})=3$$, then a + b is equal to


Question 22

If N and x are positive integers such that $$N^{N}$$ = $$2^{160}\ and \ N{^2} + 2^{N}\ $$ is an integral multiple of $$\ 2^{x}$$, then the largest possible x is


Question 23

$$\frac{1}{log_{2}100}-\frac{1}{log_{4}100}+\frac{1}{log_{5}100}-\frac{1}{log_{10}100}+\frac{1}{log_{20}100}-\frac{1}{log_{25}100}+\frac{1}{log_{50}100}$$=?


Question 24

If p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$, then the value of $$log_{s}{(pqr)}$$ is equal to


Question 25

$$\frac{log (97-56\sqrt{3})}{log \sqrt{7+4\sqrt{3}}}$$ equals which of the following?


Question 26

The real root of the equation $$2^{6x} + 2^{3x + 2} - 21 = 0$$ is