Logarithm Questions for the CAT exam are part of the Quant section in the CAT exam. Through Logarithm questions, aspirants are tested on concepts related to Formula and divisibility. The difficulty level of the Logarithm questions can be easy to moderate.

## Properties of Logarithm Questions for CAT?

- loga(bc) = logab + log ac
- loga(b/c) = logab - logac
- loga(bn)= nlogab
- log10x is common logarithm and lnx is natural logarithm
- logab=(logcb/logca) where logc denotes any logarithm base

## Logarithm Questions Tricks for the CAT Exam

- Familiarise yourself with logarithmic properties to simplify and manipulate expressions effectively.
- Solve a variety of logarithmic problems to understand different question types and their applications.
- Understand how logarithms relate to exponential functions, as many problems involve converting between these forms.

## Logarithm Questions Concepts for the CAT Exam

- Use logarithms to solve problems involving exponential growth or decay, population dynamics, interest calculations, etc.
- Understand properties like product, quotient, and power rules helps in simplifying and manipulating logarithmic expressions.
- Learn to solve equations by isolating logarithms and converting them into exponential form.

**Logarithm Practice questions for the CAT exam**

**Q 1**: For the given pair (x, y) of positive integers, such that 4x-17y=1 and x<1000 how many integer values of y satisfy the given conditions?

A. 56

B. 57

C. 58

D. 59

**Level: Easy**

**Answer: **D

**Q 2: **One-year payment to the servant is Rs. 90 plus one turban. The servant leaves after 9 months and receives Rs. 65 and turban. Then find the price of the turban

A. Rs.10

B. Rs.15

C. Rs.7.5

D. Cannot be determined

**Level: Difficult**

**Answer: **A

**Q 3**: In CAT 2007 there were 75 questions. Each correct answer was rewarded by 4 marks and each wrong answer was penalized by 1 mark. In how many different combination of correct and wrong answers is a score of 50 possible?

A. 14

B. 15

C. 16

D. None of these

**Level: Easy**

**Answer: **D

**Q 4:** How many integer solutions exist for the equation 8x – 5y = 221 such that x×y<0

A. 4

B. 5

C. 6

D. 8

**Level: Moderate**

**Answer: **C

**Must-do Logarithm questions for the CAT exam**

**Q 5**: How many integer solutions exists for the equation 11x + 15y = -1 such that both x and y are less than 100?

A. 15

B. 16

C. 17

D. 18

**Level: Difficult**

**Answer: **B

**Q 6**: The number of ordered pairs of natural numbers (a, b) satisfying the equation 2a + 3b = 100 is:

A. 13

B. 14

C. 15

D. 16

**Level: Moderate**

**Answer: **D

**Q 7:** For how many positive integral values of N, less than 40 does the equation 3a – Nb = 5, have no integer solution

A. 13

B. 14

C. 15

D. 12

**Level: Difficult**

**Answer: **A

**Q 8: **What are the number of integral solutions of the equation 7x + 3y = 123 for x,y > 0

A. 3

B. 5

C. 12

D. Infinite

**Level: Easy**

**Answer: **B

**Q 9**: The cost of 3 hamburgers, 5 milk shakes, and 1 order of fries at a certain fast food restaurant is $23.50. At the same restaurant, the cost of 5 hamburgers, 9 milk shakes, and 1 order of fries is $39.50. What is the cost of 2 hamburgers, 2 milk shakes, and 2 orders of fries at this restaurant?

A. 10

B. 15

C. 7.5

D. Cannot be determined

**Level: Moderate**

**Answer: **B

**Most Important Logarithm Question for CAT**

**Q 10:** How many integer solutions are there for the equation: |x| + |y| =7?

A. 24

B. 26

C. 14

D. None of these

**Level: Difficult**

**Answer: **D

**Q 11**: A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

A. 2 ≤ x ≤ 6

B. 5 ≤ x ≤ 8

C. 9 ≤ x ≤ 12

D. 11 ≤ x ≤ 14

**Level: Moderate**

**Answer: **B

**Q 12:** If p and Q are integers such that 7/10

B. 60

C. 30

D. 7

**Level: Easy**

**Answer: **D

**Q 13.** If x and y are positive integers and x+y+xy=54, find x+y

A. 12

B. 14

C. 15

D. 16

**Level: Difficult**

**Answer: **B

**Q 14.** A test has 20 questions, with 4 marks for a correct answer, –1 mark for a wrong answer, and no marks for an unattempted question. A group of friends took the test. If all of them scored exactly 15 marks, but each of them attempted a different number of questions, what is the maximum number of people who could be in the group?

A. 3

B. 4

C. 5

D. more than 5

**Level: Moderate**

**Answer: **B

**Find Some Previous Year Logarithm Questions for CAT**

**Q 15.** Rakesh and Manish solve an equation. In solving Rakesh commits a mistake in constant term and finds the root 8 and 2. Manish commits a mistake in the coefficient of x and finds the roots -9 and -1. Find the correct roots.

A. 9,1

B. -9,1

C. -8,-2

D. None of these

**Level: Difficult**

**Answer: **A

**Q 16:** The number of quadratic equations which are unchanged by squaring their roots is

A. 2

B. 4

C. 6

D. None of these.

**Level: Moderate**

**Answer: **D

**Q 17**. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) at x = 10?

A. -105

B. -119

C. -159

D. -110

**Level: Easy**

**Answer: **C

**Q 18.** Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum, say m, of these three integers?

A. 1 ≤ m ≤ 3

B. 4 ≤ m ≤ 6

C. 7 ≤ m ≤ 9

D. 10 ≤ m ≤ 12

**Level: Moderate**

**Answer: **A

**Q 19**: The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?

A. May 21

B. April 11

C. May 20

D. April 10

**Level: Difficult**

**Answer: **C

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