Logarithms – Introduction MCQs With Answer

Logarithms – Introduction MCQs With Answer are essential for B.Pharm students to master quantitative pharmacy topics such as pH calculations, dilution factors, and pharmacokinetic rate laws. This focused set explains core log rules, antilog use, change-of-base, and the distinction between natural logs (ln) and log base 10, all tied to pharmaceutical examples like pH, pKa, percent ionization, and first-order kinetics. Expect practical problems on converting concentration to pH, using Henderson-Hasselbalch, interpreting log-transformed data, and solving exponential decay. Clear explanations and varied practice will strengthen calculation speed and clinical reasoning for formulations and drug stability. Now let’s test your knowledge with 50 MCQs on this topic.

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

• 2
• 3
• 4
• 1

Correct Answer: 3

Q2. If pH = -log10[H+], what is the pH of a solution with [H+] = 1 x 10^-7 M?

• 6
• 7
• 8
• 1

Correct Answer: 7

Q3. Which property is true for logarithms: log(ab) equals?

• log a + log b
• log a – log b
• log a × log b
• log(a^b)

Correct Answer: log a + log b

Q4. Change of base formula for log base b of x can be written as:

• logb x = ln x + ln b
• logb x = log x / log b
• logb x = ln b / ln x
• logb x = x log b

Correct Answer: logb x = log x / log b

Q5. The antilog (base 10) of 2.5 equals:

• 10^2.5
• 2.5^10
• log10(2.5)
• e^2.5

Correct Answer: 10^2.5

Q6. Which logarithm is used in many pharmacokinetic first-order rate equations?

• Log base 2
• Log base 10 only
• Natural logarithm (ln)
• Binary logarithm

Correct Answer: Natural logarithm (ln)

Q7. If a drug follows first-order kinetics, the concentration-time plot is linear when plotted as:

• Concentration vs time
• Log concentration vs time
• 1/concentration vs time
• Time vs ln(k)

Correct Answer: Log concentration vs time

Q8. Solve for x: log10 x = 3. The value of x is:

• 0.001
• 100
• 1000
• 3

Correct Answer: 1000

Q9. Which equation relates pKa, pH, and ratio of ionized to unionized drug?

• Henderson-Hasselbalch equation
• Michaelis-Menten equation
• Arrhenius equation
• Beer-Lambert law

Correct Answer: Henderson-Hasselbalch equation

Q10. Using Henderson-Hasselbalch: For an acid with pKa 4.0, at pH 5.0 the ratio [A-]/[HA] is approximately:

• 0.1
• 1
• 10
• 100

Correct Answer: 10

Q11. log10(0.01) equals:

• -2
• 2
• -0.01
• 0.01

Correct Answer: -2

Q12. Which operation corresponds to subtracting logarithms: log a – log b equals:

• log(ab)
• log(a^b)
• log(a/b)
• log(b/a)

Correct Answer: log(a/b)

Q13. A solution has pOH = 3. What is the pH? (Assume pKw = 14)

• 11
• 3
• 7
• 14

Correct Answer: 11

Q14. If log10 A = 1.3010, A equals approximately:

• 20
• 10
• 5
• 2

Correct Answer: 20

Q15. Which is the correct identity for natural logs: ln(e^x) equals:

• x
• e^x
• ln x
• 1/x

Correct Answer: x

Q16. For radioactivity decay following first-order kinetics, amount remaining N at time t is N0 e^{-kt}. Taking natural log gives:

• ln N = ln N0 + kt
• ln N = ln N0 – kt
• log N = log N0 + kt
• ln N = k / (N0 t)

Correct Answer: ln N = ln N0 – kt

Q17. Which log expression would you use to convert a pH back to hydrogen ion concentration?

• [H+] = 10^(pH)
• [H+] = -pH
• [H+] = 10^(-pH)
• [H+] = ln(pH)

Correct Answer: [H+] = 10^(-pH)

Q18. If pH changes from 3 to 6, hydrogen ion concentration changes by a factor of:

• 3
• 1000
• 100
• 10

Correct Answer: 1000

Q19. Evaluate log10(5 × 10^3) using log properties.

• log10 5 + 3
• log10 5 × 3
• log10 5 – 3
• log10 5 / 3

Correct Answer: log10 5 + 3

Q20. For a base-10 logarithm, which statement is true?

• log10 1 = 10
• log10 10 = 1
• log10 0 = 1
• log10 100 = 1

Correct Answer: log10 10 = 1

Q21. The antilogarithm of 0.3010 (base 10) is approximately:

• 2
• 3
• 1.3010
• 0.3010

Correct Answer: 2

Q22. If concentration C decreases by first-order kinetics with k = 0.693 h^-1, the half-life t1/2 equals:

• 1.0 h
• 0.693 h
• ln 2 / k
• 2 / k

Correct Answer: ln 2 / k

Q23. Express log10(7.2 × 10^-4) as sum of log10 7.2 and exponent.

• log10 7.2 + (-4)
• log10 7.2 × (-4)
• log10 7.2 – 4
• log10 7.2 / 4

Correct Answer: log10 7.2 + (-4)

Q24. Which is true about pKa and pH when a weak acid is 50% ionized?

• pH = pKb
• pH = pKa
• pH = 2 × pKa
• pH = pKa + 1

Correct Answer: pH = pKa

Q25. Convert ln x to log10 x using constants: ln x =?

• 2.303 log10 x
• 0.4343 log10 x
• log10 x / 2.303
• log10 x + 2.303

Correct Answer: 2.303 log10 x

Q26. Which effect on pH results from diluting a strong acid solution by 10-fold (concentration decreases 10x)?

• pH decreases by 1 unit
• pH increases by 1 unit
• pH increases by 10 units
• pH unchanged

Correct Answer: pH increases by 1 unit

Q27. For a weak base, percent ionization can be estimated using log with pKb. Which equation is relevant?

• Henderson-Hasselbalch adapted for bases
• Ideal gas law
• Beer’s law
• First-order rate law

Correct Answer: Henderson-Hasselbalch adapted for bases

Q28. Which expression is equivalent to log10(1/100)?

• -2
• 2
• -0.01
• 0.01

Correct Answer: -2

Q29. If log10 A = 4.5, what is A in scientific notation?

• 3.16 × 10^4
• 4.5 × 10^1
• 10^4.5 only
• 4.5 × 10^3

Correct Answer: 3.16 × 10^4

Q30. Which logarithm property helps to handle exponents: log(a^n) equals:

• n log a
• log a^n / n
• (log a)^n
• log n × a

Correct Answer: n log a

Q31. A buffer contains equal concentrations of HA and A-. If pKa = 6.5, the buffer pH is approximately:

• 5.5
• 6.5
• 7.5
• 6.0

Correct Answer: 6.5

Q32. Which is correct: log10(0.5) approximately equals:

• -0.3010
• 0.3010
• -0.69897
• 0.69897

Correct Answer: -0.3010

Q33. In a dissolution study, plotting log remaining drug vs time yields a straight line with slope -0.05. Which is the rate constant k (natural log) approx? (Use k10 ≈ 2.303 × slope)

• 0.115 h^-1
• -0.115 h^-1
• 0.05 h^-1
• 0.023 h^-1

Correct Answer: 0.115 h^-1

Q34. Which statement is true about logarithms and multiplication?

• log(a × b) = log a – log b
• log(a × b) = log a + log b
• log(a × b) = log a × log b
• log(a × b) = (log a)^b

Correct Answer: log(a × b) = log a + log b

Q35. For a weak acid with pKa 5.0, at pH 3.0 the acid is mostly:

• ionized
• unionized
• 50% ionized
• completely ionized

Correct Answer: unionized

Q36. If log10 x = -1, x equals:

• 10
• 0.1
• -1
• 1

Correct Answer: 0.1

Q37. Which conversion is correct between ln and decimal log for a value y: log10 y = ?

• ln y × 2.303
• ln y / 2.303
• e^(ln y)
• ln(y) + 2.303

Correct Answer: ln y / 2.303

Q38. A solution with [H+] = 1 × 10^-3 M has pH:

• 3
• 11
• -3
• 0.001

Correct Answer: 3

Q39. If the log of a ratio is zero, for example log10 (A/B) = 0, then A equals:

• B
• 0
• 1
• 10B

Correct Answer: B

Q40. Which statement about logs and orders of magnitude is correct?

• Each increase of 1 in log10 corresponds to a 10-fold increase in value
• Increase of 1 in log10 corresponds to doubling
• Increase of 1 in log10 corresponds to a 100-fold change
• Logs do not relate to magnitude

Correct Answer: Each increase of 1 in log10 corresponds to a 10-fold increase in value

Q41. The pH of a 0.01 M HCl solution is approximately:

• 2
• 4
• 12
• 0.01

Correct Answer: 2

Q42. Which is the antilog (base 10) of -1.3010 approximately?

• 0.05
• 0.05 × 10^-1
• 0.05
• 0.5

Correct Answer: 0.05

Q43. For concentration units, converting 2 × 10^-6 M to log10 concentration gives approximately:

• -5.7
• -6.3
• -6.0
• -5.3

Correct Answer: -5.7

Q44. In a buffer calculation, if pH = pKa + 1, the ratio [A-]/[HA] equals approximately:

• 0.1
• 1
• 10
• 100

Correct Answer: 10

Q45. The log of the product of three numbers equals the sum of their logs. Which expresses log(abc)?

• log a + log b – log c
• log a + log b + log c
• log(a + b + c)
• log a × log b × log c

Correct Answer: log a + log b + log c

Q46. If a drug concentration declines from 100 mg/L to 10 mg/L, the change in log10 concentration is:

• +1
• -1
• -10
• +10

Correct Answer: -1

Q47. Which equation is used to find the percent ionization of a weak acid using pH and pKa?

• Percent ionization = 100 / (1 + 10^(pKa – pH))
• Percent ionization = 10^(pH – pKa)
• Percent ionization = pKa – pH
• Percent ionization = ln(10) × (pH – pKa)

Correct Answer: Percent ionization = 100 / (1 + 10^(pKa – pH))

Q48. Solve: log10(2) + log10(50) equals:

• log10(100)
• log10(1)
• log10(25)
• log10(2/50)

Correct Answer: log10(100)

Q49. When converting a biexponential decay to a linear form for parameter estimation, which transform is commonly applied?

• Square root transform
• Logarithmic transform
• Reciprocal transform only
• Exponential transform

Correct Answer: Logarithmic transform

Q50. If pKa of a drug is 8.0 and the desired pH is 6.0, the ratio [A-]/[HA] using Henderson-Hasselbalch is approximately:

• 0.01
• 100
• 0.1
• 10

Correct Answer: 0.01

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