Definition of logarithms MCQs With Answer

Definition of logarithms MCQs With Answer are essential for B. Pharm students to master mathematical tools used in pharmacokinetics, pH calculations, drug concentration decay, and analytical assays. This concise, exam-focused set explains the definition, properties, and applications of logarithms, including base-10 and natural logs, change-of-base formula, and log rules for products, quotients, and powers. Questions are tailored to pharmacy contexts—pKa, Henderson-Hasselbalch, half-life computations, dilution factors, and absorbance relationships—so learners gain practical problem-solving skills. Clear answers and stepwise reasoning improve retention and exam readiness. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What does the logarithm log_b(a) represent?

• The exponent to which b must be raised to get a
• The product of a and b
• The square root of a divided by b
• The reciprocal of a

Correct Answer: The exponent to which b must be raised to get a

Q2. If log10(1000) = x, what is x?

• 1
• 2
• 3
• 4

Correct Answer: 3

Q3. Which equation is equivalent to log_b(a) = c?

• a = b^c
• a = c^b
• b = a^c
• c = a^b

Correct Answer: a = b^c

Q4. What is the value of ln(e^3)?

• e^3
• 3
• ln 3
• 0

Correct Answer: 3

Q5. Which property of logarithms expresses log_b(xy)?

• log_b(xy) = log_b(x) + log_b(y)
• log_b(xy) = log_b(x) – log_b(y)
• log_b(xy) = log_b(x) * log_b(y)
• log_b(xy) = log_b(x)/log_b(y)

Correct Answer: log_b(xy) = log_b(x) + log_b(y)

Q6. How do you express log_b(a^k) using log rules?

• k * log_b(a)
• log_b(a) / k
• log_b(k) * a
• a^k * log_b(a)

Correct Answer: k * log_b(a)

Q7. What is the change-of-base formula for logs?

• log_b(a) = log_c(a) / log_c(b)
• log_b(a) = log_c(b) / log_c(a)
• log_b(a) = log_a(c) / log_b(c)
• log_b(a) = log_c(a) * log_c(b)

Correct Answer: log_b(a) = log_c(a) / log_c(b)

Q8. Which logarithm is most commonly used in pH calculations?

• Natural logarithm (ln)
• Base-2 logarithm (log2)
• Base-10 logarithm (log10)
• Binary logarithm (logb)

Correct Answer: Base-10 logarithm (log10)

Q9. The pH is defined as -log10[H+]. What is the pH when [H+] = 1 × 10^-7 M?

• 7
• −7
• 0.7
• 14

Correct Answer: 7

Q10. If log10(x) = 2.5, what is x?

• 2.5
• 10^2.5
• log10(2.5)
• 25

Correct Answer: 10^2.5

Q11. Which rule gives log_b(x/y)?

• log_b(x/y) = log_b(x) − log_b(y)
• log_b(x/y) = log_b(x) + log_b(y)
• log_b(x/y) = log_b(y) − log_b(x)
• log_b(x/y) = log_b(x) * log_b(y)

Correct Answer: log_b(x/y) = log_b(x) − log_b(y)

Q12. For a first-order elimination, concentration C = C0 * e^(−kt). To solve for k, which transformation uses logs?

• ln(C/C0) = −kt
• log10(C) = −kt
• C0 = ln(C) + kt
• k = log10(C0/C)/t

Correct Answer: ln(C/C0) = −kt

Q13. If half-life t1/2 = ln(2)/k, which log is used to derive this?

• Natural logarithm (ln)
• Base-10 logarithm (log10)
• Base-2 logarithm (log2)
• No logarithm is used

Correct Answer: Natural logarithm (ln)

Q14. What is log10(0.001)?

• −3
• 3
• −0.001
• 0.001

Correct Answer: −3

Q15. Which statement about logarithms is false?

• log_b(1) = 0 for any b>0, b≠1
• log_b(b) = 1 for any b>0, b≠1
• log_b(0) is defined
• Logs convert multiplication into addition

Correct Answer: log_b(0) is defined

Q16. In spectroscopy, absorbance A = log10(I0/I). What does this imply?

• Absorbance is proportional to the log of incident to transmitted intensity ratio
• Absorbance equals the difference I0 − I
• Absorbance is independent of light intensity
• Absorbance is the square root of I0/I

Correct Answer: Absorbance is proportional to the log of incident to transmitted intensity ratio

Q17. Convert log_e(50) to base-10: log10(50) = ln(50)/ln(10). Which formula justifies this?

• Change-of-base formula
• Power rule
• Product rule
• Quotient rule

Correct Answer: Change-of-base formula

Q18. If log2(8) = x, what is x?

• 3
• 2
• 8
• 0.125

Correct Answer: 3

Q19. Which log identity simplifies log_b(1/a)?

• log_b(1/a) = −log_b(a)
• log_b(1/a) = log_b(a)
• log_b(1/a) = 1/log_b(a)
• log_b(1/a) = a * log_b(1)

Correct Answer: log_b(1/a) = −log_b(a)

Q20. In Henderson-Hasselbalch, pH = pKa + log10([A−]/[HA]). This uses which log property?

• Logarithm of a quotient
• Logarithm of a product
• Logarithm of a power
• Change-of-base

Correct Answer: Logarithm of a quotient

Q21. Solve for x: log10(x) = −2. Which x is correct?

• 0.01
• 100
• −2
• 2

Correct Answer: 0.01

Q22. Which is true for natural logs and exponentials?

• ln(e^y) = y
• e^(ln y) = ln(y)^e
• ln(e) = e
• ln(y^e) = e * y

Correct Answer: ln(e^y) = y

Q23. If a drug concentration falls from 100 mg/L to 25 mg/L in one hour, log10(C0/C) = ? for use in rate equations.

• log10(100/25) = log10(4) ≈ 0.602
• log10(25/100) = −0.602
• log10(100 − 25) = log10(75)
• log10(100 * 25)

Correct Answer: log10(100/25) = log10(4) ≈ 0.602

Q24. Which log base converts easily between decibels and power ratios?

• Base-10 logarithm (log10)
• Natural logarithm (ln)
• Base-2 logarithm (log2)
• Base-euler (loge)

Correct Answer: Base-10 logarithm (log10)

Q25. What is log10(5 × 10^3)?

• log10(5) + 3
• log10(5) − 3
• log10(5) * 3
• 3 / log10(5)

Correct Answer: log10(5) + 3

Q26. Which is the inverse function of y = log_b(x)?

• y = b^x
• y = ln(x)
• y = log_b(1/x)
• y = x^b

Correct Answer: y = b^x

Q27. For small changes, logs help linearize exponential decay. Which plot linearizes a first-order decay?

• ln(C) vs time
• C vs time
• log10(time) vs C
• sqrt(C) vs time

Correct Answer: ln(C) vs time

Q28. Which value equals log10(1)?

• 0
• 1
• 10
• Undefined

Correct Answer: 0

Q29. If k = 0.693 h^−1, what is the half-life t1/2? (t1/2 = ln2/k)

• 1 hour
• 0.693 hours
• ln2 hours
• 2 hours

Correct Answer: 1 hour

Q30. Which is correct: log_b(a^m * a^n) = ?

• log_b(a^(m+n)) = (m+n) log_b(a)
• log_b(a^(m+n)) = m log_b(a) − n log_b(a)
• log_b(a^m * a^n) = log_b(a^m) / log_b(a^n)
• log_b(a^m * a^n) = log_b(a)^m + log_b(a)^n

Correct Answer: log_b(a^(m+n)) = (m+n) log_b(a)

Q31. Which expression is equivalent to log10(0.5) + log10(2)?

• log10(1) = 0
• log10(1) = 1
• log10(4)
• log10(0.25)

Correct Answer: log10(1) = 0

Q32. In pharmacokinetics, if concentration ratio C1/C2 = 10, log10(C1/C2) = ?

• 1
• 10
• 0.1
• −1

Correct Answer: 1

Q33. What is log10(9.0 × 10^2)?

• log10(9.0) + 2
• log10(9.0) − 2
• 9.0 + 2
• 902

Correct Answer: log10(9.0) + 2

Q34. Which of these is undefined in real numbers?

• log10(−1)
• log10(0.1)
• log10(1)
• ln(2)

Correct Answer: log10(−1)

Q35. If pKa = 4.76 and pH = 5.76, what is the ratio [A−]/[HA]? (Henderson-Hasselbalch)

• 10
• 0.1
• 1
• 100

Correct Answer: 10

Q36. For log_b(a) where b = 10 and a = 100, which is true?

• log10(100) = 2
• log10(100) = 10
• log10(100) = 0.5
• log10(100) = −2

Correct Answer: log10(100) = 2

Q37. Which operation is easier after taking logarithms of multiplicative experimental errors?

• Summation of errors
• Multiplication of errors
• Exponentiation of errors
• Integration of errors

Correct Answer: Summation of errors

Q38. What is the result of log10(2) + log10(5)?

• log10(10) = 1
• log10(7)
• log10(0.4)
• log10(25)

Correct Answer: log10(10) = 1

Q39. Which of the following helps compute drug dilution factors using logs?

• logarithm rules for products and quotients
• trigonometric identities
• matrix inversion
• complex arithmetic

Correct Answer: logarithm rules for products and quotients

Q40. If ln(A) = 4, what is A?

• e^4
• 4e
• ln(4)
• 16

Correct Answer: e^4

Q41. Which expression uses the power rule correctly?

• log_b(a^3) = 3 log_b(a)
• log_b(a^3) = log_b(3a)
• log_b(a^3) = log_b(a) / 3
• log_b(a^3) = log_b(a)^3

Correct Answer: log_b(a^3) = 3 log_b(a)

Q42. A drug’s concentration follows C = C0 * 10^(−kt). Taking log10 gives which linear relation?

• log10(C) = log10(C0) − kt
• log10(C) = log10(C0) + kt
• log10(C) = kt − log10(C0)
• log10(C) = k + log10(C0)

Correct Answer: log10(C) = log10(C0) − kt

Q43. Which is true about log base b when b>1?

• log_b(x) is increasing with x
• log_b(x) is decreasing with x
• log_b(x) is periodic
• log_b(x) is constant

Correct Answer: log_b(x) is increasing with x

Q44. Which log is commonly used in kinetics to linearize data plotted as log concentration vs time?

• Natural log (ln)
• Base-2 log (log2)
• Binary log
• No log is used

Correct Answer: Natural log (ln)

Q45. What is log10(4 × 10^−3)?

• log10(4) − 3
• log10(4) + 3
• −log10(4) + 3
• 4 − 3

Correct Answer: log10(4) − 3

Q46. If log_b(a) = 2 and log_b(c) = 3, what is log_b(a^2 * c)?

• 2*2 + 3 = 7
• 2 + 3 = 5
• 4 + 3 = 7
• 2*3 = 6

Correct Answer: 4 + 3 = 7

Q47. How to solve for time t when C = C0 e^(−kt) and concentrations are known?

• t = −(1/k) ln(C/C0)
• t = k ln(C/C0)
• t = ln(C0 * C)/k
• t = ln(k)/ln(C/C0)

Correct Answer: t = −(1/k) ln(C/C0)

Q48. Which statement correctly uses logs for dilution: a 1:1000 dilution changes concentration by?

• −3 log10 units
• +3 log10 units
• −1000 log10 units
• 0.001 log10 units

Correct Answer: −3 log10 units

Q49. In experiment calibration, plotting log(concentration) vs signal often yields:

• A straight line if response is power-law
• A sine wave
• A random scatter only
• An exponential curve always

Correct Answer: A straight line if response is power-law

Q50. Which best summarizes why logs are important in B.Pharm mathematics?

• They linearize exponentials, simplify multiplicative relationships, and aid pH, kinetics, and analytical calculations
• They eliminate the need for units
• They always convert data to integers
• They are only used for theoretical proofs, not practical work

Correct Answer: They linearize exponentials, simplify multiplicative relationships, and aid pH, kinetics, and analytical calculations

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