Class 9 Maths Chapter 2 – Logarithms MCQs (FBISE) - MCQs

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Description: Practice Class 9 Maths Chapter 2 Logarithms MCQs according to the latest FBISE syllabus. These exam-oriented multiple-choice questions cover the concept of logarithms, laws of logarithms, common and natural logarithms, and logarithmic tables.

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1. If $\log_a b = c$ , then:

A) $a^b=c$
B) $a^c=b$
C) $b^c=a$
D) $c^a=b$

2. The logarithm is the inverse operation of:

A) Exponentiation
B) Addition
C) Division
D) Subtraction

3. The value of $\log_{10} 1000$ is:

A) 1
B) 2
C) 10
D) 3

4. The base of a common logarithm is:

A) $e$
B) 2
C) 10
D) 100

5. The natural logarithm has base:

A) 10
B) $e$
C) 2
D) 5

6. $\log_a 1$ is equal to:

A) 0
B) 1
C) $a$
D) Undefined

7. $\log_a a$ is equal to:

A) 0
B) $a$
C) 1
D) 10

8. Which law is correct?

A) $\log(M+N)=\log M+\log N$
B) $\log(M-N)=\log M-\log N$
C) $\log(MN)=\log M \times \log N$
D) $\log(MN)=\log M+\log N$

9. $\log_{10} 0.1$ is:

A) -1
B) 0
C) 1
D) 10

10. The quotient law of logarithms is:

A) $\log(MN)=\log M+\log N$
B) $\log\left(\frac{M}{N}\right)=\log M-\log N$
C) $\log(M^n)=n+\log M$
D) $\log(M+N)=\log M+\log N$

11. Which of the following is undefined?

A) $\log_{10}100$
B) $\log_{2}8$
C) $\log_{5}25$
D) $\log_{10}(-5)$

12. $\log_{2} 8$ is equal to:

A) 3
B) 2
C) 4
D) 8

13. The power law states:

A) $\log(MN)=\log M+\log N$
B) $\log(M/N)=\log M-\log N$
C) $\log(M^n)=n\log M$
D) $\log(M+n)=\log M+n$

14. The characteristic of $\log_{10}(500)$ is:

A) 0
B) 2
C) 3
D) -2

15. Logarithmic tables are mainly used to:

A) Draw graphs
B) Find derivatives
C) Solve geometry problems
D) Simplify lengthy numerical calculations

16. Which statement about logarithms is true?

A) The argument of a logarithm must be positive.
B) The argument may be zero.
C) The argument may be negative.
D) The base can be zero.

17. If $10^x=100$ , then $x$ equals:

A) 1
B) 10
C) 2
D) 100

18. If $\log_{10} x = 4$ , then $x$ is:

A) 40
B) 10000
C) 4000
D) 104

19. Which expression is equivalent to $\log_a (MN)$ ?

A) $\log_a M + \log_a N$
B) $\log_a M - \log_a N$
C) $\log_a(M+N)$
D) $\log_a(MN)^2$

20. The base of a logarithm must be:

A) Negative
B) Zero
C) Equal to 1
D) Positive and not equal to 1

21. $\log_{10} 1 =$

A) 10
B) -1
C) 0
D) 1

22. Which property converts multiplication into addition?

A) Power law
B) Product law
C) Quotient law
D) Identity law

23. If $\log_3 27 = x$ , then $x$ equals:

A) 3
B) 9
C) 2
D) 27

24. Which logarithm is commonly written simply as $\log x$ ?

A) Base 2
B) Base $e$
C) Base 10
D) Base 5

25. The logarithm of a negative number in the real number system is:

A) Positive
B) Zero
C) Negative
D) Undefined

26. If $\log_a b = c$ , then $b$ can be written as:

A) $a^c$
B) $c^a$
C) $a+b$
D) $ac$

27. Which law is used to simplify $\log(M^5)$ ?

A) Product law
B) Power law
C) Quotient law
D) Commutative law

28. The characteristic of $\log_{10}(50)$ is:

A) -1
B) 0
C) 2
D) 1

29. Which instrument was traditionally used before calculators for logarithmic calculations?

A) Logarithm tables
B) Compass
C) Divider
D) Protractor

30. $\log_{10}(100000)$ equals:

A) 3
B) 4
C) 5
D) 6

31. Which expression is equal to $\log_a \left(\frac{M}{N}\right)$ ?

A) $\log_a M + \log_a N$
B) $\log_a M - \log_a N$
C) $\log_a(M-N)$
D) $\frac{\log_a M}{\log_a N}$

32. If $10^2 = 100$ , then $\log_{10}(100)$ is:

A) 10
B) 0
C) 100
D) 2

33. Logarithms are especially useful for simplifying:

A) Multiplication and division of large numbers
B) Drawing circles
C) Constructing triangles
D) Solving linear inequalities only

34. The argument of a logarithm must always be:

A) Zero
B) Negative
C) Positive
D) Equal to the base

35. If $\log_{10} x = 0$ , then the value of $x$ is:

A) 10
B) 1
C) 0
D) -1

36. Which expression is equivalent to $\log_5 125$ ?

A) 2
B) 4
C) 5
D) 3

37. The logarithm of the base itself is always:

A) 1
B) 0
C) Equal to the base
D) Undefined

38. Which logarithmic law is represented by $\log(M^n)=n\log(M)$ ?

A) Product law
B) Quotient law
C) Power law
D) Identity law

39. If $\log_{10}(0.01)=x$ , then $x$ equals:

A) -1
B) -2
C) 2
D) 1

40. Which quantity is called the argument of a logarithm?

A) The number whose logarithm is taken
B) The base of the logarithm
C) The exponent only
D) The characteristic

41. Which of the following is equal to $\log_{10}(10^7)$ ?

A) 10
B) 1
C) 70
D) 7

42. In common logarithms, the mantissa of numbers having the same significant digits is:

A) Different
B) Negative
C) The same
D) Zero

43. Which of the following is true for logarithmic tables?

A) They usually list mantissas for positive numbers
B) They contain only natural logarithms
C) They are used only in geometry
D) They cannot be used for powers

44. The value of $\log_{100}100$ is:

A) 0
B) 1
C) 2
D) 100

45. If $\log_a b=c$ , then $c$ represents the:

A) Base
B) Argument
C) Mantissa
D) Exponent to which the base is raised

46. Which of the following satisfies $\log_{10}10000$ ?

A) 4
B) 3
C) 5
D) 2

47. Before electronic calculators, logarithms were widely used by:

A) Artists only
B) Historians only
C) Scientists and engineers
D) Musicians only

48. Which expression simplifies to $2\log_a x$ ?

A) $\log_a(2x)$
B) $\log_a(x^2)$
C) $\log_a(x+2)$
D) $\log_a(x/2)$

49. Which statement about logarithms is correct?

A) Every real number has a real logarithm.
B) The base may be 1.
C) The argument may be zero.
D) The base must be positive and not equal to 1.

50. The primary purpose of studying logarithms is to:

A) Simplify exponential relationships and complex calculations
B) Replace algebra completely
C) Measure geometric angles
D) Find areas of polygons only

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