Common logarithms MCQs With Answer

Common logarithms MCQs With Answer provide B. Pharm students essential practice in logarithmic calculations used across pharmaceutical sciences. This concise, Student-friendly post covers key topics: common logarithm properties, pH and pKa computations, Beer–Lambert absorbance, first-order kinetics, dilution factors and concentration conversions. Mastering log10 rules helps pharmacy students solve drug stability, buffer design, assay interpretation and pharmacokinetic problems accurately. These multiple-choice questions emphasize applied examples and calculation shortcuts to build speed and confidence for exams and lab work. Targeted keywords: common logarithms, log10, pH calculations, pharmacokinetics, Beer–Lambert law, buffer, B. Pharm MCQs. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the value of the common logarithm log10(1000)?

• 2
• 3
• 4
• -3

Correct Answer: 3

Q2. What is log10(0.01)?

• -1
• -0.01
• -2
• 2

Correct Answer: -2

Q3. Which identity is true for common logarithms?

• log10(ab) = log10 a × log10 b
• log10(ab) = log10 a + log10 b
• log10(a/b) = log10 a + log10 b
• log10(a^b) = log10 a + b

Correct Answer: log10(ab) = log10 a + log10 b

Q4. How do you express log10(x) in terms of natural logarithm ln(x)?

• log10(x) = 2.303 × ln(x)
• log10(x) = ln(x) / 2.303
• log10(x) = ln(x) + 2.303
• log10(x) = ln(x) – 2.303

Correct Answer: log10(x) = ln(x) / 2.303

Q5. If [H+] = 1 × 10^-7 M, what is the pH?

• 14
• 7
• -7
• 0

Correct Answer: 7

Q6. For an acid with pKa = 4.76, what is the ratio [A-]/[HA] when pH = pKa + 1?

• 0.1
• 1
• 10
• 100

Correct Answer: 10

Q7. Beer–Lambert law relates absorbance A to transmittance T as:

• A = log10 T
• A = -log10 T
• T = -log10 A
• A = 10^T

Correct Answer: A = -log10 T

Q8. If transmittance T = 0.9, what is the absorbance A (approx)?

• 0.046
• 0.9
• 1.0
• 0.105

Correct Answer: 0.046

Q9. Which expression gives pH from hydrogen ion concentration?

• pH = log10 [H+]
• pH = -log10 [H+]
• pH = ln [H+]
• pH = 10^[H+]

Correct Answer: pH = -log10 [H+]

Q10. If pH = 3.5, what is [H+] approximately?

• 3.16 × 10^-4 M
• 3.5 × 10^-3 M
• 3.16 × 10^-5 M
• 1 × 10^-3.5 M

Correct Answer: 3.16 × 10^-4 M

Q11. Which log rule allows computing log10(a^b)?

• log10(a^b) = log10 a + log10 b
• log10(a^b) = b × log10 a
• log10(a^b) = a × log10 b
• log10(a^b) = (log10 a)^b

Correct Answer: log10(a^b) = b × log10 a

Q12. Change in pH by 1 unit corresponds to what change in [H+]?

• 2-fold change
• 10-fold change
• 100-fold change
• No change

Correct Answer: 10-fold change

Q13. For a ten-fold dilution of drug solution, the log10 concentration changes by:

• +1
• -1
• 0
• +10

Correct Answer: -1

Q14. Which formula correctly relates log10(Ct/C0) to first-order rate constant k and time t?

• log10(Ct/C0) = -kt
• log10(Ct/C0) = -kt / 2.303
• log10(Ct/C0) = -2.303 kt
• log10(Ct/C0) = kt / 2.303

Correct Answer: log10(Ct/C0) = -kt / 2.303

Q15. Using the first-order relation, how long to reduce concentration to 10% if k = 0.1 h^-1?

• 2.303 h
• 23.03 h
• 10 h
• 0.2303 h

Correct Answer: 23.03 h

Q16. Convert ln(x) to log10(x) using the constant 2.303. Which is correct?

• ln(x) = 0.4343 × log10(x)
• log10(x) = 2.303 × ln(x)
• ln(x) = 2.303 × log10(x)
• log10(x) = ln(x) × 0.4343

Correct Answer: ln(x) = 2.303 × log10(x)

Q17. If absorbance A = 1.0, transmittance T equals:

• 100%
• 10%
• 1%
• 0.1%

Correct Answer: 10%

Q18. For a weak acid where pH = pKa, what is the ratio [A-]/[HA]?

• 10
• 1
• 0.1
• 100

Correct Answer: 1

Q19. Which relation derives from Henderson–Hasselbalch? (Rearranged form)

• [A-]/[HA] = 10^(pKa – pH)
• [A-]/[HA] = 10^(pH – pKa)
• [HA]/[A-] = 10^(pH – pKa)
• [A-] + [HA] = 10^(pH – pKa)

Correct Answer: [A-]/[HA] = 10^(pH – pKa)

Q20. If pKa = 4.76 and pH = 6.76, [A-]/[HA] equals:

• 10
• 0.01
• 100
• 1

Correct Answer: 100

Q21. What is log10(5 × 10^4) simplified using log rules?

• log10 5 + 4
• log10 5 – 4
• 4 × log10 5
• 5 + log10 4

Correct Answer: log10 5 + 4

Q22. If log10(x) = 2.3, what is x (approx)?

• 200
• 199.5
• 2.3
• 10^2

Correct Answer: 199.5

Q23. If pH changes from 7.0 to 5.0, by what factor does [H+] change?

• 2-fold decrease
• 10-fold decrease
• 100-fold increase
• 1000-fold increase

Correct Answer: 100-fold increase

Q24. Compute pH for [H+] = 2 × 10^-4 M (approx).

• 3.30
• 3.70
• 4.30
• 3.00

Correct Answer: 3.70

Q25. Evaluate log10(3.2 × 10^-4) (approx).

• -3.495
• -4.505
• -3.205
• -4.495

Correct Answer: -3.495

Q26. Which is the decimal value of log10(2)?

• 0.3010
• 0.4771
• 0.69897
• 1.0000

Correct Answer: 0.3010

Q27. Using logs, which expression gives time t for first-order decay from C0 to Ct?

• t = (2.303/k) × log10(Ct/C0)
• t = (2.303/k) × log10(C0/Ct)
• t = (k/2.303) × log10(C0/Ct)
• t = (k/2.303) × log10(Ct/C0)

Correct Answer: t = (2.303/k) × log10(C0/Ct)

Q28. If absorbance increases by 1 unit, transmittance changes by what factor?

• Increases 10-fold
• Decreases 10-fold
• No change
• Decreases by 1%

Correct Answer: Decreases 10-fold

Q29. What is log10(1) equal to?

• 1
• 0
• -1
• Undefined

Correct Answer: 0

Q30. If log10(x) = -3, what is x?

• 1000
• 0.001
• -3
• 3

Correct Answer: 0.001

Q31. Which identity is correct: log10(1/x) = ?

• log10 x
• -log10 x
• 1/log10 x
• log10 x + 1

Correct Answer: -log10 x

Q32. For concentration ratio C1/C2 = 100, what is log10(C1) – log10(C2)?

• 0.01
• 2
• -2
• 100

Correct Answer: 2

Q33. Which is the approximate value of log10(0.5)?

• -0.3010
• 0.3010
• -0.6990
• 0.6990

Correct Answer: -0.3010

Q34. If pH = 8, what is pOH at 25°C and [OH-] (approx)?

• pOH = 6, [OH-] = 1 × 10^-6 M
• pOH = 6, [OH-] = 1 × 10^-8 M
• pOH = 14, [OH-] = 1 × 10^-14 M
• pOH = 6, [OH-] = 1 × 10^-12 M

Correct Answer: pOH = 6, [OH-] = 1 × 10^-8 M

Q35. Which statement is correct about pKa and pKb for a conjugate acid–base pair at 25°C?

• pKa + pKb = 0
• pKa + pKb = 7
• pKa + pKb = 14
• pKa + pKb = 1

Correct Answer: pKa + pKb = 14

Q36. If log10(7.5) ≈ 0.8751, what is 10^0.8751 (approx)?

• 7.5
• 0.8751
• 10
• 1

Correct Answer: 7.5

Q37. For a solution whose absorbance is 2.00, what percent transmittance is observed?

• 1%
• 0.01%
• 10%
• 0.1%

Correct Answer: 1%

Q38. Calculate pH if [H+] = 5 × 10^-8 M (approx).

• 7.30
• 8.30
• 6.70
• 7.70

Correct Answer: 7.30

Q39. Which equation correctly expresses A = εlc in log-based spectrophotometry terms?

• A = -log10(I/I0)
• A = log10(I/I0)
• A = I/I0
• A = 10^(I/I0)

Correct Answer: A = -log10(I/I0)

Q40. What is log10(100^0.5)?

• 1
• 2
• 0.5
• 10

Correct Answer: 1

Q41. If concentration decreases from 1.0 to 0.001, the change in log10 concentration is:

• +3
• -3
• -0.003
• +0.003

Correct Answer: -3

Q42. Solve: log10(2.5 × 10^-2) (approx).

• -1.602
• -2.602
• -0.602
• -1.398

Correct Answer: -1.602

Q43. Which expresses the Henderson–Hasselbalch equation?

• pH = pKb + log([A-]/[HA])
• pH = pKa + log([A-]/[HA])
• pH = pKa – log([A-]/[HA])
• pH = -log([A-]/[HA])

Correct Answer: pH = pKa + log([A-]/[HA])

Q44. For first-order kinetics, what does a plot of log10 concentration vs. time yield?

• A parabola
• A straight line with slope -k/2.303
• An exponential curve
• A straight line with slope k

Correct Answer: A straight line with slope -k/2.303

Q45. If a drug solution shows A = 0.699 and standard 1.00 mg/mL has A = 0.699, what is sample concentration?

• 0.699 mg/mL
• 1.00 mg/mL
• 0.100 mg/mL
• 10 mg/mL

Correct Answer: 1.00 mg/mL

Q46. Which numeric equals log10(e) approximately?

• 0.4343
• 2.303
• 0.3010
• 1.000

Correct Answer: 0.4343

Q47. If pH = 4.00, what is [H+]?

• 1 × 10^-4 M
• 4 × 10^-1 M
• 1 × 10^4 M
• 4 × 10^-4 M

Correct Answer: 1 × 10^-4 M

Q48. Which transformation is useful to linearize exponential decay data for drug degradation?

• Plot concentration vs. time
• Plot ln concentration vs. time or log10 concentration vs. time
• Plot square of concentration vs. time
• Plot concentration^2 vs. time

Correct Answer: Plot ln concentration vs. time or log10 concentration vs. time

Q49. For a buffer where pH − pKa = 3, the ratio [A-]/[HA] is:

• 3
• 10
• 1000
• 0.001

Correct Answer: 1000

Q50. What is the pH of 0.01 M HCl (strong acid, full dissociation)?

• 1
• 2
• 10
• 0.01

Correct Answer: 2

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