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CAT Logarithms, Surds and Indices questions are the important questions frequently appearing in the CAT examination. Practising mocks for CAT where you'll get a fair idea of how questions are asked, and type of questions asked in CAT Exam. 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 |
| 2023 | 4 |
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.
1. Formula: Properties of logarithm
$$$\log_{a}{1} = 0$$$ $$$\log_{a}{xy} = \log_{a}{x}+\log_{a}{y}$$$ $$$\log_{a}{b}^{c} = c \log_{a}{b}$$$ $$${b}^{\log_{b}{x}} = x$$$ $$${x}^{\log_{b}{y}} = {y}^{\log_{b}{x}} $$$ $$${\log_{a}{\sqrt[n]{b}}} = \dfrac{\log_{a}{b}}{n} $$$ $$${\log_{a}{b}} = \dfrac{\log_{c}{b}}{\log_{c}{a}}$$$ $$${\log_{a}{b}}*{\log_{b}{a}}= 1$$$ $$$a^m\times\ a^n=a^{m+n}$$$ $$$\frac{a^m\ \ }{a^n}\ =a^{m-n}$$$ $$$\left(a^m\right)^{^n}=a^{m\times\ n}$$$ $$$\left(a\times\ b\right)^m\ =a^m\times\ b^m$$$ $$$a^{-m}=\ \frac{1}{a^m}$$$ $$$a^{\frac{m}{n}}=\sqrt[\ n]{a^m}$$$
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
correct answer:-4
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
correct answer:-3
If $$\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$$, then $$\sqrt{10x+9}$$ is equal to
correct answer:-3
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
correct answer:-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
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
