Logarithm — 21 Aptitude Questions and Answers with Explanations

Logarithm — Questions and Answers

Logarithms convert multiplication into addition, which is exactly why exams like them: a question that looks like heavy arithmetic becomes a two-line sum. You need four laws and the meaning of the base. In competitive papers the base is 10 unless stated otherwise, and log 2 ≈ 0.3010 with log 3 ≈ 0.4771 are the two values worth memorising.

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Logarithm— Concepts, Formulas & Shortcuts

log_a x = y means aʸ = x. The base a must be positive and not equal to 1.
log(mn) = log m + log n; log(m/n) = log m − log n; log(mⁿ) = n log m.
log_a 1 = 0 and log_a a = 1 for every valid base.
Change of base: log_a b = log b / log a.
Standard values (base 10): log 2 ≈ 0.3010, log 3 ≈ 0.4771, log 5 = 1 − log 2 ≈ 0.6990.
The characteristic of a log is the integer part and the mantissa is the decimal part.

Logarithm Practice Questions with Answers

Attempt each question first, then open the explanation. All 21 questions below are free to read and require no signup.

Q1.The value of log₁₀ 100 is:
Easy
- A1
- B2
- C10
- D100
+Show Answer & Explanation
Answer: B. 2
Explanation: 10² = 100, so the logarithm is 2.
Logarithm question 1 of 21
Q2.The value of log_a 1 (for any valid base a) is:
Easy
- A0
- B1
- Ca
- DUndefined
+Show Answer & Explanation
Answer: A. 0
Explanation: a⁰ = 1 for every non-zero a, so the logarithm of 1 is always 0.
Logarithm question 2 of 21
Q3.The value of log₂ 32 is:
Easy
- A4
- B5
- C6
- D16
+Show Answer & Explanation
Answer: B. 5
Explanation: 2⁵ = 32, so log₂ 32 = 5.
Logarithm question 3 of 21
Q4.log(ab) is equal to:
Easy
- Alog a × log b
- Blog a + log b
- Clog a − log b
- Da log b
+Show Answer & Explanation
Answer: B. log a + log b
Explanation: The product rule converts multiplication inside the log into addition outside it.
Logarithm question 4 of 21
Q5.If log 2 = 0.3010, then log 8 equals:
Moderate
- A0.6020
- B0.9030
- C1.2040
- D2.4080
+Show Answer & Explanation
Answer: B. 0.9030
Explanation: log 8 = log 2³ = 3 × 0.3010 = 0.9030.
Logarithm question 5 of 21
Q6.The value of log₃ 81 is:
Easy
- A3
- B4
- C9
- D27
+Show Answer & Explanation
Answer: B. 4
Explanation: 3⁴ = 81, so the logarithm is 4.
Logarithm question 6 of 21
Q7.The value of log_a a is:
Easy
- A0
- B1
- Ca
- D1/a
+Show Answer & Explanation
Answer: B. 1
Explanation: a¹ = a, so the logarithm of the base to its own base is always 1.
Logarithm question 7 of 21
Q8.The value of log₁₀ 1000 is:
Easy
- A2
- B3
- C10
- D100
+Show Answer & Explanation
Answer: B. 3
Explanation: 10³ = 1000, so the logarithm is 3.
Logarithm question 8 of 21
Q9.The value of log₅ 125 is:
Easy
- A2
- B3
- C5
- D25
+Show Answer & Explanation
Answer: B. 3
Explanation: 5³ = 125, so log₅ 125 = 3.
Logarithm question 9 of 21
Q10.log(m/n) is equal to:
Easy
- Alog m × log n
- Blog m + log n
- Clog m − log n
- Dlog m ÷ log n
+Show Answer & Explanation
Answer: C. log m − log n
Explanation: The quotient rule turns division inside the log into subtraction outside it.
Logarithm question 10 of 21
Q11.If log 3 = 0.4771, then log 9 equals:
Moderate
- A0.6021
- B0.9542
- C1.4313
- D2.3855
+Show Answer & Explanation
Answer: B. 0.9542
Explanation: log 9 = log 3² = 2 × 0.4771 = 0.9542.
Logarithm question 11 of 21
Q12.The value of log₂ 1 is:
Easy
- A0
- B1
- C2
- DUndefined
+Show Answer & Explanation
Answer: A. 0
Explanation: 2⁰ = 1, so the logarithm of 1 to any base is 0.
Logarithm question 12 of 21
Q13.If log₁₀ x = 2, then x equals:
Easy
- A10
- B20
- C100
- D1000
+Show Answer & Explanation
Answer: C. 100
Explanation: The base is 10, so x = 10² = 100.
Logarithm question 13 of 21
Q14.The value of log₄ 64 is:
Moderate
- A2
- B3
- C4
- D16
+Show Answer & Explanation
Answer: B. 3
Explanation: 4³ = 64, so the logarithm is 3.
Logarithm question 14 of 21
Q15.The value of log₁₀ 10 is:
Easy
- A0
- B1
- C10
- D100
+Show Answer & Explanation
Answer: B. 1
Explanation: 10¹ = 10, so the logarithm is 1.
Logarithm question 15 of 21
Q16.The value of log₂ 16 is:
Easy
- A2
- B3
- C4
- D8
+Show Answer & Explanation
Answer: C. 4
Explanation: 2⁴ = 16, so log₂ 16 = 4.
Logarithm question 16 of 21
Q17.The value of log₁₀ 0.1 is:
Moderate
- A−1
- B0
- C1
- D10
+Show Answer & Explanation
Answer: A. −1
Explanation: 10⁻¹ = 0.1, so the logarithm is −1.
Logarithm question 17 of 21
Q18.log(m³) is equal to:
Easy
- A3 + log m
- B3 log m
- C(log m)³
- Dlog 3 × log m
+Show Answer & Explanation
Answer: B. 3 log m
Explanation: The power rule brings the exponent to the front: log(mⁿ) = n log m.
Logarithm question 18 of 21
Q19.If log 2 = 0.3010, then log 4 equals:
Moderate
- A0.4771
- B0.6020
- C0.9030
- D1.2040
+Show Answer & Explanation
Answer: B. 0.6020
Explanation: log 4 = log 2² = 2 × 0.3010 = 0.6020.
Logarithm question 19 of 21
Q20.The value of log₆ 36 is:
Easy
- A1
- B2
- C3
- D6
+Show Answer & Explanation
Answer: B. 2
Explanation: 6² = 36, so the logarithm is 2.
Logarithm question 20 of 21
Q21.log 100 + log 10 (base 10) equals:
Moderate
- A2
- B3
- C10
- D1000
+Show Answer & Explanation
Answer: B. 3
Explanation: 2 + 1 = 3. Equivalently log(100 × 10) = log 1000 = 3.
Logarithm question 21 of 21

Logarithm — Frequently Asked Questions

What is the default base in competitive exam logarithm questions?+

Base 10, unless the question specifies otherwise. Natural logs (base e) rarely appear in aptitude papers, though they are common in engineering ones.

How do I compute log 8 if I only know log 2?+

Write 8 as 2³ and apply the power rule: log 8 = 3 log 2 = 3 × 0.3010 = 0.9030.

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