Logarithms – Algebra MCQs – T4Tutorials.com

Question 1:

\[
\text{If } \log_2 8 = x, \text{ what is the value of } x?
\]
\[
\text{(a) } 2, \quad \text{(b) } 3, \quad \text{(c) } 4, \quad \text{(d) } 5
\]
Answer: B

Question 2:

\[
\text{If } \log_5 (25) = x, \text{ then } x \text{ is:}
\]
\[
\text{(a) } 2, \quad \text{(b) } 5, \quad \text{(c) } 3, \quad \text{(d) } 1
\]
Answer: A

Question 3:

\[
\text{Solve for } x: \quad \log_3 x = 4
\]
\[
\text{(a) } 81, \quad \text{(b) } 27, \quad \text{(c) } 12, \quad \text{(d) } 9
\]
Answer: A

Question 4:

\[
\text{If } \log 10 = 1, \text{ what is } \log 1000?
\]
\[
\text{(a) } 3, \quad \text{(b) } 10, \quad \text{(c) } 2, \quad \text{(d) } 1000
\]
Answer: A

Question 5:

\[
\text{Which property of logarithms is represented by } \log(ab) = \log a + \log b?
\]
\[
\text{(a) } \text{Power Rule}, \quad \text{(b) } \text{Product Rule}, \quad \text{(c) } \text{Quotient Rule}, \quad \text{(d) } \text{Inverse Rule}
\]
Answer: B

Question 6:

\[
\text{If } \log 3 = x \text{ and } \log 5 = y, \text{ express } \log 15 \text{ in terms of } x \text{ and } y.
\]
\[
\text{(a) } x + y, \quad \text{(b) } x – y, \quad \text{(c) } xy, \quad \text{(d) } x/y
\]
Answer: A

Question 7:

\[
\text{If } \log 2 = 0.3010, \text{ then } \log 32 \text{ is:}
\]
\[
\text{(a) } 1.505, \quad \text{(b) } 2.3010, \quad \text{(c) } 1.698, \quad \text{(d) } 1.999
\]
Answer: A

Question 8:

\[
\text{The value of } \log_4 16 \text{ is:}
\]
\[
\text{(a) } 2, \quad \text{(b) } 3, \quad \text{(c) } 4, \quad \text{(d) } 5
\]
Answer: A

Question 9:

\[
\text{What is the value of } \log_7 49?
\]
\[
\text{(a) } 3, \quad \text{(b) } 2, \quad \text{(c) } 7, \quad \text{(d) } 4
\]
Answer: B

Question 10:

\[
\text{If } \log 7 = x, \text{ then } \log 49 \text{ in terms of } x \text{ is:}
\]
\[
\text{(a) } 2x, \quad \text{(b) } x/2, \quad \text{(c) } x+1, \quad \text{(d) } x-1
\]
Answer: A

Question 11:

\[
\text{If } \log_a x = 5 \text{ and } \log_a y = 3, \text{ what is } \log_a(x/y)?
\]
\[
\text{(a) } 2, \quad \text{(b) } 8, \quad \text{(c) } -2, \quad \text{(d) } 15
\]
Answer: A

Question 12:

\[
\text{What is the domain of } f(x) = \log(x-3)?
\]
\[
\text{(a) } x > 0, \quad \text{(b) } x > 3, \quad \text{(c) } x \geq 3, \quad \text{(d) } x < 3
\]
Answer: B

Question 13:

\[
\text{If } \log_3 (x+1) = 2, \text{ then } x = ?
\]
\[
\text{(a) } 8, \quad \text{(b) } 9, \quad \text{(c) } 10, \quad \text{(d) } 11
\]
Answer: A

Question 14:

\[
\text{Solve for } x: \quad \log_4 (x+3) = 3
\]
\[
\text{(a) } 60, \quad \text{(b) } 61, \quad \text{(c) } 62, \quad \text{(d) } 63
\]
Answer: B

Question 15:

\[
\text{Which logarithm property is used in } \log \left( \frac{a}{b} \right) = \log a – \log b?
\]
\[
\text{(a) } \text{Product Rule}, \quad \text{(b) } \text{Quotient Rule}, \quad \text{(c) } \text{Power Rule}, \quad \text{(d) } \text{Inverse Rule}
\]
Answer: B

Question 16:

\[
\text{What is the base of the natural logarithm } \ln(x)?
\]
\[
\text{(a) } 2, \quad \text{(b) } 10, \quad \text{(c) } e, \quad \text{(d) } 3
\]
Answer: C

Question 17:

\[
\text{If } \ln e^5 = x, \text{ then } x = ?
\]
\[
\text{(a) } 5, \quad \text{(b) } e^5, \quad \text{(c) } 1, \quad \text{(d) } 10
\]
Answer: A

Question 18:

\[
\text{If } 2\log x = \log 25, \text{ find } x.
\]
\[
\text{(a) } 5, \quad \text{(b) } 10, \quad \text{(c) } 25, \quad \text{(d) } 2.5
\]
Answer: A

Logarithms – Algebra MCQs
By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025