# 25+ CAT Logarithms Questions With Video Solutions & Formulas

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.

## CAT Logarithms Weightage Over Past 3 Years

 Year Weightage 2023 1 2022 1 2021 1

## Tips for CAT Logarithms Questions

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.

## CAT Logarithms Formulas PDF

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

$$\log_{a}{1} = 0$$$$$\log_{a}{xy} = \log_{a}{x}+\log_{a}{y}$$$ $$\log_{a}{b}^{c} = c \log_{a}{b}$$$$${b}^{\log_{b}{x}} = x$$$ $${x}^{\log_{b}{y}} = {y}^{\log_{b}{x}}$$$$${\log_{a}{\sqrt[n]{b}}} = \dfrac{\log_{a}{b}}{n}$$$ $${\log_{a}{b}} = \dfrac{\log_{c}{b}}{\log_{c}{a}}$$$$${\log_{a}{b}}*{\log_{b}{a}}= 1$$$ $$a^m\times\ a^n=a^{m+n}$$$$$\frac{a^m\ \ }{a^n}\ =a^{m-n}$$$ $$\left(a^m\right)^{^n}=a^{m\times\ n}$$$$$\left(a\times\ b\right)^m\ =a^m\times\ b^m$$$ $$a^{-m}=\ \frac{1}{a^m}$$$$$a^{\frac{m}{n}}=\sqrt[\ n]{a^m}$$$

• Logarithms can be used to quickly find the number of digits in an exponent.

## CAT 2023 Logarithms questions

#### Question 1

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 2

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

## CAT 2021 Logarithms questions

#### Question 1

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 2

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

#### Question 3

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

## CAT 2020 Logarithms questions

#### Question 1

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

#### Question 2

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

#### Question 3

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

#### Question 4

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

#### Question 5

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

## CAT 2019 Logarithms questions

#### Question 1

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

#### Question 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

## CAT 2018 Logarithms questions

#### Question 1

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

#### Question 2

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

#### Question 3

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

#### Question 4

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

#### Question 5

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

## CAT 2017 Logarithms questions

#### Question 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

#### Question 2

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

#### Question 3

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