MATHS Quiz

Maths Objective Questions: Exponential & Logarithmic Functions

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by Chandra Shekhar
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Maths Objective Questions: Exponential & Logarithmic Functions

Maths Objective Questions: Exponential & Logarithmic Functions

For UP TGT Exam Preparation

1. What is the value of e0?
A) 0
B) 1
C) e
D) ∞
Answer: B) 1
Explanation: Any non-zero number raised to the power of 0 is 1, so e0 = 1.
2. Simplify log10(100).
A) 1
B) 2
C) 10
D) 100
Answer: B) 2
Explanation: log10(100) = log10(102) = 2.
3. What is the value of eln(x)?
A) x
B) e
C) ln(x)
D) 1
Answer: A) x
Explanation: By the property of exponents and logarithms, eln(x) = x for x > 0.
4. Solve for x: log2(8) = x.
A) 2
B) 3
C) 4
D) 8
Answer: B) 3
Explanation: Since 8 = 23, log2(8) = log2(23) = 3.
5. What is the derivative of ex?
A) ex
B) x ex-1
C) ln(x)
D) ex / x
Answer: A) ex
Explanation: The derivative of ex with respect to x is ex.
6. Evaluate log4(64).
A) 2
B) 3
C) 4
D) 6
Answer: B) 3
Explanation: Since 64 = 43, log4(64) = log4(43) = 3.
7. Simplify log5(25).
A) 1
B) 2
C) 5
D) 25
Answer: B) 2
Explanation: Since 25 = 52, log5(25) = log5(52) = 2.
8. What is the value of 2log2(3)?
A) 2
B) 3
C) 6
D) 9
Answer: B) 3
Explanation: By properties of logarithms, 2log2(3) = 3.
9. What is the inverse of y = ex?
A) y = ln(x)
B) x = ln(y)
C) y = log10(x)
D) y = e-x
Answer: A) y = ln(x)
Explanation: The inverse of y = ex is y = ln(x), as ln(ex) = x.
10. Solve: e2x = 5.
A) x = ln(5)/2
B) x = ln(5)
C) x = 5/2
D) x = 2 ln(5)
Answer: A) x = ln(5)/2
Explanation: Take ln of both sides: 2x = ln(5), so x = ln(5)/2.
11. Simplify log3(81).
A) 2
B) 3
C) 4
D) 9
Answer: C) 4
Explanation: Since 81 = 34, log3(81) = log3(34) = 4.
12. What is log10(0.001)?
A) -3
B) -2
C) 3
D) 2
Answer: A) -3
Explanation: Since 0.001 = 10-3, log10(0.001) = log10(10-3) = -3.
13. Solve: 2x = 16.
A) 2
B) 3
C) 4
D) 5
Answer: C) 4
Explanation: Since 16 = 24, 2x = 24 implies x = 4.
14. What is the domain of y = ln(x)?
A) x > 0
B) x ≥ 0
C) All real numbers
D) x ≠ 0
Answer: A) x > 0
Explanation: The natural logarithm is defined only for positive values of x.
15. Simplify log2(1/8).
A) -3
B) -2
C) 2
D) 3
Answer: A) -3
Explanation: Since 1/8 = 2-3, log2(1/8) = log2(2-3) = -3.
16. What is the derivative of ln(x)?
A) 1/x
B) x
C) ln(x)/x
D) ex
Answer: A) 1/x
Explanation: The derivative of ln(x) with respect to x is 1/x.
17. Solve: log5(x) = 2.
A) 5
B) 10
C) 25
D) 50
Answer: C) 25
Explanation: log5(x) = 2 implies x = 52 = 25.
18. Evaluate 3log3(5).
A) 3
B) 5
C) 15
D) 9
Answer: B) 5
Explanation: 3log3(5) = 5 by the inverse property of logarithms.
19. What is the integral of ex dx?
A) ex + C
B) ln(x) + C
C) x ex + C
D) ex/x + C
Answer: A) ex + C
Explanation: The integral of ex is ex + C.
20. Simplify log10(1000).
A) 2
B) 3
C) 4
D) 10
Answer: B) 3
Explanation: Since 1000 = 103, log10(1000) = 3.
21. Solve: ex = 10.
A) ln(10)
B) log10(e)
C) 10
D) e10
Answer: A) ln(10)
Explanation: Take ln of both sides: x = ln(10).
22. What is the range of y = ex?
A) All real numbers
B) y > 0
C) y ≥ 0
D) y < 0
Answer: B) y > 0
Explanation: The exponential function ex is always positive for all real x.
23. Simplify log2(16x).
A) 4 + log2(x)
B) 4 log2(x)
C) log2(x) + 16
D) 2 + log2(x)
Answer: A) 4 + log2(x)
Explanation: log2(16x) = log2(16) + log2(x) = log2(24) + log2(x) = 4 + log2(x).
24. Solve: log3(x) + log3(x-2) = 1.
A) 3
B) 4
C) 5
D) No solution
Answer: A) 3
Explanation: log3(x(x-2)) = 1, so x(x-2) = 31 = 3. Solve x2 – 2x – 3 = 0, x = 3 (x = -1 invalid).
25. What is the value of log10(1)?
A) 0
B) 1
C) -1
D) Undefined
Answer: A) 0
Explanation: log10(1) = 0, as 100 = 1.
26. What is the integral of 1/x dx?
A) ln|x| + C
B) ex + C
C) x-1 + C
D) 1/ln(x) + C
Answer: A) ln|x| + C
Explanation: The integral of 1/x is ln|x| + C.
27. Solve: 4x = 64.
A) 2
B) 3
C) 4
D) 6
Answer: B) 3
Explanation: Since 64 = 43, 4x = 43 implies x = 3.
28. Simplify log5(x2).
A) 2 log5(x)
B) log5(x)
C) x log5(2)
D) 5 log2(x)
Answer: A) 2 log5(x)
Explanation: log5(x2) = 2 log5(x) by the power rule.
29. What is the value of eln(2)?
A) 1
B) 2
C) e
D) ln(2)
Answer: B) 2
Explanation: eln(2) = 2 by the inverse property.
30. Solve: log2(x+1) = 3.
A) 7
B) 8
C) 9
D) 10
Answer: A) 7
Explanation: log2(x+1) = 3 implies x+1 = 23 = 8, so x = 7.
31. What is the base of the natural logarithm?
A) 10
B) e
C) 2
D) 5
Answer: B) e
Explanation: The natural logarithm has base e ≈ 2.718.
32. Simplify log10(x/100).
A) log10(x) – 2
B) log10(x) + 2
C) 2 log10(x)
D) log10(x/2)
Answer: A) log10(x) – 2
Explanation: log10(x/100) = log10(x) – log10(100) = log10(x) – 2.
33. Solve: 52x = 25.
A) 1
B) 2
C) 3
D) 4
Answer: A) 1
Explanation: Since 25 = 52, 52x = 52 implies 2x = 2, so x = 1.
34. What is the derivative of 2x?
A) 2x ln(2)
B) 2x
C) x 2x-1
D) ln(x) 2x
Answer: A) 2x ln(2)
Explanation: The derivative of ax is ax ln(a), so for 2x, it’s 2x ln(2).
35. Evaluate log3(1/27).
A) -3
B) -2
C) 2
D) 3
Answer: A) -3
Explanation: Since 1/27 = 3-3, log3(1/27) = log3(3-3) = -3.
36. Solve: ln(x) = 0.
A) 0
B) 1
C) e
D) Undefined
Answer: B) 1
Explanation: ln(x) = 0 implies x = e0 = 1.
37. What is the value of log10(105)?
A) 3
B) 4
C) 5
D) 6
Answer: C) 5
Explanation: log10(105) = 5 by the definition of logarithms.
38. Simplify e2ln(x).
A) x
B) x2
C) 2x
D) ln(x2)
Answer: B) x2
Explanation: e2ln(x) = (eln(x))2 = x2.
39. Solve: 3x+1 = 27.
A) 1
B) 2
C) 3
D) 4
Answer: B) 2
Explanation: Since 27 = 33, 3x+1 = 33 implies x+1 = 3, so x = 2.
40. What is the derivative of x ln(x)?
A) ln(x) + 1
B) ln(x)
C) 1/x + ln(x)
D) x (1/x)
Answer: C) 1/x + ln(x)
Explanation: Using the product rule, d/dx[x ln(x)] = ln(x) + x(1/x) = ln(x) + 1.
41. Evaluate log2(32).
A) 3
B) 4
C) 5
D) 6
Answer: C) 5
Explanation: Since 32 = 25, log2(32) = 5.
42. Solve: e3x = e6.
A) 1
B) 2
C) 3
D) 6
Answer: B) 2
Explanation: e3x = e6 implies 3x = 6, so x = 2.
47. What is the base of the common logarithm?
A) 2
B) e
C) 10
D) 5
Answer: C) 10
Explanation: The common logarithm, denoted log(x), has a base of 10.
48. Simplify log2(8x3).
A) 3 + 3log2(x)
B) 3log2(x)
C) 8 + log2(x)
D) log2(x) + 3
Answer: A) 3 + 3log2(x)
Explanation: log2(8x3) = log2(8) + log2(x3) = log2(23) + 3log2(x) = 3 + 3log2(x).
49. Solve for x: log5(x) + log5(x + 4) = 1.
A) 1
B) 2
C) 3
D) No solution
Answer: A) 1
Explanation: log5(x(x + 4)) = 1, so x(x + 4) = 5. Solving x2 + 4x – 5 = 0 gives x = 1 (x = -5 is invalid).
50. What is the value of log3(9) + log3(27)?
A) 3
B) 4
C) 5
D) 6
Answer: C) 5
Explanation: log3(9) = log3(32) = 2, log3(27) = log3(33) = 3, so 2 + 3 = 5.

Prepared for UP TGT Exam | Modern Maths Practice

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