PRE CALCULUS Exponential and Logarithmic Functions 2

Question 1

What is log_2(32) equal to?

Accepted Answer

5

Answer

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)?

Accepted Answer

Product rule

Answer

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)

Accepted Answer

2

Answer

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)?

Accepted Answer

7

Answer

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)?

Accepted Answer

x > 4

Answer

The argument of a logarithm must be positive, so x − 4 > 0, which gives x > 4.

PRE CALCULUS Practice Test