Top CAT Quant Logarithms Questions [Download PDF]

by Naveen Neredimalli Wed 15 May 2024 05:46 PM 66
Top_CAT_Quant_Logarithms_Questions

Logarithms are a key topic in the CAT Quantitative Ability (QA) section, consistently appearing in exams over the years. Typically, 1-2 straightforward questions on logarithms are included, making it essential for students to master the basics and practice thoroughly. Reviewing CAT past papers with detailed video solutions is highly recommended.

To practice important logarithm questions for the CAT exam, you can download a PDF of previous years' questions with video solutions—no sign-up required. Additionally, take 3 free CAT mock tests to assess your current level and identify your strengths and weaknesses.

Question 1

If $$\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$$, then $$\sqrt{10x+9}$$ is equal to


Question 2

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


Question 3

If $$\log_{a}{30}=A,\log_{a}({\frac{5}{3}})=-B$$ and $$\log_2{a}=\frac{1}{3}$$, then $$\log_3{a}$$ equals


Question 4

If $$5 - \log_{10}\sqrt{1 + x} + 4 \log_{10} \sqrt{1 - x} = \log_{10} \frac{1}{\sqrt{1 - x^2}}$$, then 100x equals


Question 5

Let x and y be positive real numbers such that
$$\log_{5}{(x + y)} + \log_{5}{(x - y)} = 3,$$ and $$\log_{2}{y} - \log_{2}{x} = 1 - \log_{2}{3}$$. Then $$xy$$ equals


Question 6

For a real number a, if $$\frac{\log_{15}{a}+\log_{32}{a}}{(\log_{15}{a})(\log_{32}{a})}=4$$ then a must lie in the range


Question 7

If $$(\sqrt{\frac{7}{5}})^{3x-y}=\frac{875}{2401}$$ and $$(\frac{4a}{b})^{6x-y}=(\frac{2a}{b})^{y-6x}$$, for all non-zero real values of a and b, then the value of $$x+y$$ is


Question 8

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


Question 9

If $$\log_{2}[3+\log_{3} \left\{4+\log_{4}(x-1) \right\}]-2=0$$ then 4x equals


Question 10

If $$x=(4096)^{7+4\sqrt{3}}$$, then which of the following equals to 64?


Question 11

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


Question 12

$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals


Question 13

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


Question 14

If x is a positive real number such that $$x^8 + \left(\frac{1}{x}\right)^8 = 47$$, then the value of $$x^9 + \left(\frac{1}{x}\right)^9$$ is


Question 15

If $$x$$ and $$y$$ are positive real numbers such that $$\log_{x}(x^2 + 12) = 4$$ and $$3 \log_{y} x = 1$$, then $$x + y $$ equals


Question 16

If $$\log_4m + \log_4n = \log_2(m + n)$$ where m and n are positive real numbers, then which of the following must be true?


Question 17

The value of $$\log_{a}({\frac{a}{b}})+\log_{b}({\frac{b}{a}})$$, for $$1<a\leq b$$ cannot be equal to


Question 18

If $$\log_{4}{5}=(\log_{4}{y})(\log_{6}{\sqrt{5}})$$, then y equals


Question 19

If $$(5.55)^x = (0.555)^y = 1000$$, then the value of $$\frac{1}{x} - \frac{1}{y}$$ is


Question 20

Consider the equation $$\log_5(x - 2) = 2 \log_{25}(2x - 4)$$, where x is a real number.
For how many different values of x does the given equation hold?

Show Answer Explanation

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