PRE CALCULUS Exponential and Logarithmic Functions 2 — Questions and Answers
Question 1: What is log_2(32) equal to?
- 4
- 5 (Correct answer)
- 6
- 16
Correct answer: 5
log_2(32) = 5 because 2^5 = 32.
Question 2: Which property of logarithms states that log_b(MN) = log_b(M) + log_b(N)?
- Power rule
- Quotient rule
- Product rule (Correct answer)
- Change of base rule
Correct answer: Product rule
The product rule of logarithms states that the log of a product equals the sum of the logs: log_b(MN) = log_b(M) + log_b(N).
Question 3: Simplify: log_5(125) − log_5(5)
- 1
- 2 (Correct answer)
- 3
- 25
Correct answer: 2
Using the quotient rule: log_5(125/5) = log_5(25) = 2, since 5^2 = 25.
Question 4: What is the natural logarithm ln(e^7)?
- e^7
- 7e
- 7 (Correct answer)
- 1/7
Correct answer: 7
ln(e^7) = 7 because the natural logarithm and e^x are inverse functions, so ln(e^x) = x.
Question 5: What is the domain of f(x) = log_3(x − 4)?
- x > 0
- x > 4 (Correct answer)
- x ≥ 4
- all real numbers
Correct answer: x > 4
The argument of a logarithm must be positive, so x − 4 > 0, which gives x > 4.
Question 6: Using the change of base formula, log_7(50) equals which of the following?
- ln(7)/ln(50)
- log(50)/log(7) (Correct answer)
- log(7)/log(50)
- ln(50) − ln(7)
Correct answer: log(50)/log(7)
The change of base formula gives log_b(a) = log(a)/log(b), so log_7(50) = log(50)/log(7).
Question 7: Which of the following is equivalent to log_b(x^4)?
- 4 + log_b(x)
- log_b(4x)
- 4·log_b(x) (Correct answer)
- log_b(x)/4
Correct answer: 4·log_b(x)
The power rule of logarithms states log_b(x^n) = n·log_b(x), so log_b(x^4) = 4·log_b(x).
