CAT Logarithms, Surds and Indices topic is the part of quantitative aptitude section. No direct questions can be expected from this topic, however, the questions might be framed using the basic concepts of this topic in combination with some other topic. All the important and direct formulas for the quick calculations are provided in the article below. Download CAT Question Papes

In CAT 2021, candidates can expect around 1 to 2 questions in this section. Based on the updated exam pattern of CAT a total of 26 will be asked from the quantitative aptitude section. Therefore, preparation of this topic will help in scoring 3 to 6 marks in the exam. The difficulty level of this section can be rated easy in comparison to other topics of CAT QA Syllabus. Read the article to check basic concepts, important formulas and solved sample questions.

Basic Concepts of CAT Logarithms, Surds and Indices

In the below section, the basic definition of Logarithms, Surds and Indices are mentioned.

• In Mathematics, logarithm can be defined as the reverse function of the exponent or the power to which a base must be raised to relent the number that is already given. For example, x can be considered as the logarithm of n to the base b if bx = n, where one can write x = logb n. In another way 23 = 8; so, 3 is the logarithm of 8 to base 2, or 3 = log2 8.
• In Mathematics, surds are classified as the value in square root that are not converted in a simple way into the entire numbers or integers. Surds can be defined as the irrational number. For example, √2, √3, √5, etc. can be taken as the value of these are not simplified.
• In Mathematics, index or power, is the number that appears on the top of a number or letter. The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself. As an example,

3 1 = 3

3 2 = 3 × 3 = 9

3 3 = 3 × 3 × 3 = 27

3 4 = 3 × 3 × 3 × 3 = 81

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CAT Important Formulas for Logarithms, Surds and Indices

There are certain common laws that students must use when solving questions pertaining to Logarithms, Indices, and Surds

Common Formulas for Logarithms and Examples

Common Rule and Properties for Surds

Types of Surds

1. Pure Surds- Surds which have only irrational parts are known as Pure Surds.
2. Mixed Surds- Surds which have rational as well as irrational parts are known as mixed surds.
3. Compound Surds- Complex surds are formed by the addition and subtraction of two or more surds.
4. Similar Surd- Surd which has common factors amongst them is called Similar Surd.
5. Binomial Surd- The formation of a single surd by two other surds from Binomial Surds.

Common rules of Indices and Examples

CAT Logarithms, Surds and Indices Solved Question

Some solved question for CAT Logarithms, Surds and Indices are given below

Ques. What is the outcome of 2log4 29?

1. 4.86
2. 4.32
3. 3.44
4. 4.30

Correct Answer: (A)

Ques. What is the value of x in log2x = 6?

1. 24
2. 64
3. 65
4. 62

Correct Answer: (B)

Ques. What is the solution for log 5x + log (2x+3) = 1 + 2log (3-x) , when x<3?

1. 6/5
2. 6/4
3. 6/2
4. 6/6

Correct Answer: (A)

Ques. Find out the solution for 163/2 + 16-3/2.

1. 4097/64
2. 4082/62
3. 4123/63
4. 4455/73

Correct Answer: (A)

Ques. What is the conjugate of 5√3 + √2?

1. 5√3 – √2
2. 5√3 – √5
3. 5√9 – √2
4. 5√7 – √3

Correct Answer: (A)

Ques. If log2X + log4X = log0.25√6 and x > 0, then x is

1. 6-1/6
2. 61/6
3. 3-1/3
4. 61/3

Correct Answer: (A)

Ques. When log9 (3log2 (1 + log3 (1 + 2log2x))) = 12. What will be the value for x?

1. 4
2. 12
3. 1
4. 2

Correct Answer: (D)

Ques. Find out the value of √x + 2√x.

1. 3√x
2. 4√x
3. 2√x
4. 5√x

Correct Answer: (A)

Ques. If log1227 = a, log916 = b, Find out the outcome of log8108.

1. 2(a+3)3b
2. 2(a+3)3a
3. 2(b+3)3a
4. 2(b+3)3b

Correct Answer: (D)

Ques. log3x + logx3 = 174. Calculate the value of x.

1. 34
2. 31/4
3. 34 or 31/4
4. 31/3

Correct Answer: (C)

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CAT Preparation Tips for Logarithms, Surds and Indices

Here, some tricks and tips for the preparation of CAT Logarithms, Surds and Indices are mentioned below.

• Keep a note of all the important formulas.
• Apply for all the questions related to it
• Before calculation, understand the value and carefully read the question
• Practice all the question from the previous year ‘s paper
• Give mock test as many times as possible