CAT Logarithms, Surds and Indices questions are the important questions frequently appearing in the CAT examination. These questions require a solid understanding of fundamental concepts. To help the aspirants, we have compiled all the questions from this topic that appear in the previous CAT papers, along with the video solutions for every question explained in detail by the CAT toppers. One can download them in a PDF format or take them in a test format. Click on the link below to download the CAT Logarithms, Surds and Indices questions with detailed video solutions PDF.
Year | Weightage |
2022 | 1 |
2021 | 3 |
2020 | 7 |
2019 | 4 |
2018 | 7 |
Logarithms, surds and indices questions are frequently asked in the previous CAT papers. In order to ace this topic and solve the CAT questions, aspirants must be well-versed in the basic concepts and formulas. To help the aspirants, we have made a PDF which consists of all the formulas, tips and tricks to solve these questions. Every formula in this PDF is very important. Click on the below link to download the CAT Logarithms, Surds and Indices Formulas PDF.
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
correct answer:-14
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
correct answer:-3
If $$\log_{2}[3+\log_{3} \left\{4+\log_{4}(x-1) \right\}]-2=0$$ then 4x equals
correct answer:-5
If $$5 - \log_{10}\sqrt{1 + x} + 4 \log_{10} \sqrt{1 - x} = \log_{10} \frac{1}{\sqrt{1 - x^2}}$$, then 100x equals
correct answer:-99
If Y is a negative number such that $$2^{Y^2({\log_{3}{5})}}=5^{\log_{2}{3}}$$, then Y equals to:
correct answer:-2
If $$\log_{a}{30}=A,\log_{a}({\frac{5}{3}})=-B$$ and $$\log_2{a}=\frac{1}{3}$$, then $$\log_3{a}$$ equals
correct answer:-1
The value of $$\log_{a}({\frac{a}{b}})+\log_{b}({\frac{b}{a}})$$, for $$1<a\leq b$$ cannot be equal to
correct answer:-3
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
correct answer:-3
If $$x=(4096)^{7+4\sqrt{3}}$$, then which of the following equals to 64?
correct answer:-3
If $$\log_{4}{5}=(\log_{4}{y})(\log_{6}{\sqrt{5}})$$, then y equals
correct answer:-36
$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals
correct answer:-24
If $$(5.55)^x = (0.555)^y = 1000$$, then the value of $$\frac{1}{x} - \frac{1}{y}$$ is
correct answer:-1
The real root of the equation $$2^{6x} + 2^{3x + 2} - 21 = 0$$ is
correct answer:-2
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
correct answer:-3
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
correct answer:-1
If x is a positive quantity such that $$2^{x}=3^{\log_{5}{2}}$$. then x is equal to
correct answer:-4
If $$\log_{12}{81}=p$$, then $$3(\dfrac{4-p}{4+p})$$ is equal to
correct answer:-4
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
correct answer:-10
$$\frac{1}{log_{2}100}-\frac{1}{log_{4}100}+\frac{1}{log_{5}100}-\frac{1}{log_{10}100}+\frac{1}{log_{20}100}-\frac{1}{log_{25}100}+\frac{1}{log_{50}100}$$=?
correct answer:-1
If p$$^{3}$$ = q$$^{4}$$ = r$$^{5}$$ = s$$^{6}$$, then the value of $$log_{s}{(pqr)}$$ is equal to
correct answer:-1
Given that $$x^{2018}y^{2017}=\frac{1}{2}$$, and $$x^{2016}y^{2019}=8$$, then value of $$x^{2}+y^{3}$$ is
correct answer:-4
If $$\log_{2}({5+\log_{3}{a}})=3$$ and $$\log_{5}({4a+12+\log_{2}{b}})=3$$, then a + b is equal to
correct answer:-1
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
correct answer:-4
If x is a real number such that $$\log_{3}5= \log_{5}(2 + x)$$, then which of the following is true?
correct answer:-4
The value of $$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$ is equal to
correct answer:-3
If $$9^{2x-1}-81^{x-1}=1944$$, then $$x$$ is
correct answer:-2
If $$9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$, then $$x$$ is
correct answer:-1
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
correct answer:-3
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?
correct answer:-5
If x = -0.5, then which of the following has the smallest value?
correct answer:-2
Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?
correct answer:-2
If x >= y and y > 1, then the value of the expression $$log_x (x/y) + log_y (y/x)$$ can never be
correct answer:-4
Let $$u = ({\log_2 x})^2 - 6 {\log_2 x} + 12$$ where x is a real number. Then the equation $$x^u = 256$$, has
correct answer:-2
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
correct answer:-4
If $$f(x) = \log \frac{(1+x)}{(1-x)}$$, then f(x) + f(y) is
correct answer:-2
If $$\log_{2}{\log_{7}{(x^2 - x+37)}}$$ = 1, then what could be the value of ‘x’?
correct answer:-3
Which of the following is true?
correct answer:-2
Find the value of $$\frac{1}{1 + \frac{1}{3-\frac{4}{2+\frac{1}{3-\frac{1}{2}}}}}$$ + $$\frac{3}{3 - \frac{4}{3+\frac{1}{2-\frac{1}{2}}}}$$
correct answer:-2
$$2^{73}-2^{72}-2^{71}$$ is the same as
correct answer:-3