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Logarithms is one of the key topics in the CAT Quantitative Ability (QA) Section, have consistently appeared in CAT exams over the years. The questions on logarithms are usually easy, and hence students should not ignore this topic. Typically, 1-2 questions are included in the new format of the CAT Quant section. It is essential that you know the basics of the CAT Logarithms well and practice the 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 Logs questions for the CAT Exam. If you want to practice these important Logarithms questions. 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.
Note: No Sign-up is required to download the questions PDF
Year | Weightage |
| 2023 | 1 |
2022 | 1 |
2021 | 1 |
Logarithm for CAT - Tip 1: Questions based on Logs appear in the CAT test almost every year. It is one of the easiest topics and hence should not be avoided. Based on our analysis of the CAT Previous Papers, 1-2 questions are frequently asked from Logarithms.
Logarithm for CAT - Tip 2: Understand the CAT Syllabus and check out the Previous Year Papers of CAT. Practising Previous year's CAT questions on logarithms helps you understand the type of questions that appear from the Logs concepts. You can check out CAT Previous Year logarithm questions with detailed solutions here.
Logarithm for CAT - Tip 3: The Logarithms topic does not include too many concepts to master, and hence can be learned easily. Getting yourself acquainted with the basics of Logs will help you solve the problems. You can learn all the Important Logarithm Formulas for CAT, here.
Logarithm for CAT - Tip 4: Given the 2-hour format of the CAT, Speed becomes very important. You need to solve more questions in lesser time. Hence, choosing the easy questions becomes very crucial. Logarithms are one of those easy questions, and thus, cannot be missed on the exam. Do checkout the CAT Formula Handbook which includes all the key CAT Quant Formulas.
Important Lograthim formulas for CAT exam are given here. Logarithms 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 $$x$$ 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
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
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 $$\log_{4}{5}=(\log_{4}{y})(\log_{6}{\sqrt{5}})$$, 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
The real root of the equation $$2^{6x} + 2^{3x + 2} - 21 = 0$$ is
correct answer:-2
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
$$\frac{1}{log_{2}100}-\frac{1}{log_{4}100}+\frac{1}{log_{5}100}-\frac{1}{log_{10}100}+\frac{1}{log_{20}100}-\frac{1}{log_{25}100}+\frac{1}{log_{50}100}$$=?
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
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
