Q.1 If log₂ 8 = x, then the value of x is?
2
3
8
4
Explanation - Since 2³ = 8, log₂ 8 = 3.
Correct answer is: 3
Q.2 If log₅ 25 = x, find x.
1
2
5
25
Explanation - Since 5² = 25, log₅ 25 = 2.
Correct answer is: 2
Q.3 If log₁₀ 1000 = x, find x.
2
3
10
1000
Explanation - 10³ = 1000, so log₁₀ 1000 = 3.
Correct answer is: 3
Q.4 If logₐ b = 3 and a = 2, find b.
6
8
9
12
Explanation - b = a³ = 2³ = 8.
Correct answer is: 8
Q.5 Simplify: log₂ 32 - log₂ 4
2
3
4
5
Explanation - log₂ 32 - log₂ 4 = log₂ (32/4) = log₂ 8 = 3.
Correct answer is: 3
Q.6 If logₓ 16 = 4, find x.
2
4
8
16
Explanation - x⁴ = 16, so x = 2.
Correct answer is: 2
Q.7 Simplify: log₃ 81
2
3
4
5
Explanation - 3⁴ = 81, so log₃ 81 = 4.
Correct answer is: 4
Q.8 If log₁₀ x = 2, find x.
10
100
1000
20
Explanation - 10² = 100, so x = 100.
Correct answer is: 100
Q.9 Evaluate log₄ 64
2
3
4
5
Explanation - 4³ = 64, so log₄ 64 = 3.
Correct answer is: 3
Q.10 Simplify: log₆ 36
2
3
4
5
Explanation - 6² = 36, so log₆ 36 = 2.
Correct answer is: 2
Q.11 If logₓ 81 = 4, find x.
2
3
9
16
Explanation - x⁴ = 81 ⇒ x = 3.
Correct answer is: 3
Q.12 Simplify: log₁₀ 0.01
-1
-2
0
2
Explanation - 0.01 = 10⁻², so log₁₀ 0.01 = -2.
Correct answer is: -2
Q.13 If log₂ x = 5, find x.
16
32
64
25
Explanation - 2⁵ = 32, so x = 32.
Correct answer is: 32
Q.14 Simplify: log₅ 125 - log₅ 25
1
2
3
4
Explanation - log₅ 125 - log₅ 25 = log₅ (125/25) = log₅ 5 = 1.
Correct answer is: 1
Q.15 If log₁₀ 2 = 0.301, find log₁₀ 200.
2.301
2.3010
3.301
3.3010
Explanation - log₁₀ 200 = log₁₀ (2×100) = log₁₀ 2 + log₁₀ 100 = 0.301 + 2 = 2.301.
Correct answer is: 2.301
Q.16 Evaluate log₉ 27
3/2
2/3
1/2
1/3
Explanation - 27 = 3³ = (9)^(3/2), so log₉ 27 = 3/2.
Correct answer is: 3/2
Q.17 If logₓ 16 = 2, find x.
2
4
8
16
Explanation - x² = 16 ⇒ x = 4.
Correct answer is: 4
Q.18 Simplify: logₐ b + logₐ c
logₐ (b/c)
logₐ (b×c)
logₐ (b+c)
logₐ (b-c)
Explanation - Property of logarithms: logₐ b + logₐ c = logₐ (b×c).
Correct answer is: logₐ (b×c)
Q.19 If logₓ 49 = 2, find x.
5
7
9
14
Explanation - x² = 49 ⇒ x = 7.
Correct answer is: 7
Q.20 Simplify: log₁₀ 50 - log₁₀ 2
25
48
52
100
Explanation - log₁₀ 50 - log₁₀ 2 = log₁₀ (50/2) = log₁₀ 25.
Correct answer is: 25
Q.21 Evaluate log₂ 0.5
-1
0
1
2
Explanation - 0.5 = 1/2 = 2⁻¹, so log₂ 0.5 = -1.
Correct answer is: -1
Q.22 If log₁₀ x = -1, find x.
0.1
0.01
1
10
Explanation - 10⁻¹ = 0.1 ⇒ x = 0.1.
Correct answer is: 0.1
Q.23 Simplify: logₐ (1/a)
1
-1
0
a
Explanation - logₐ (1/a) = logₐ (a⁻¹) = -1.
Correct answer is: -1
Q.24 If logₓ 32 = 5, find x.
2
4
5
8
Explanation - x⁵ = 32 ⇒ x = 2.
Correct answer is: 2
Q.25 Simplify: log₃ 9 + log₃ 27
3
5
6
4
Explanation - log₃ 9 + log₃ 27 = log₃ (9×27) = log₃ 243 = 5.
Correct answer is: 5