PRE CALCULUS Exponential and Logarithmic Functions 3

Question 1

Solve for x: 2^x = 64

Accepted Answer

x = 6

Answer

Since 2^6 = 64, the solution is x = 6.

Question 2

Solve for x: log_3(x) = 4

Accepted Answer

x = 81

Answer

Converting to exponential form: x = 3^4 = 81.

Question 3

A population doubles every 10 years. If the initial population is 5,000, what is the population after 30 years?

Accepted Answer

40,000

Answer

After 30 years, the population doubles 3 times: 5,000 × 2^3 = 5,000 × 8 = 40,000.

Question 4

Solve for x: ln(x) + ln(x − 2) = ln(8)

Accepted Answer

x = 4

Answer

Using the product rule: ln(x(x−2)) = ln(8), so x^2 − 2x = 8, giving x = 4 (rejecting x = −2 since ln requires positive arguments).

Question 5

What is the inverse function of f(x) = e^(x−1)?

Accepted Answer

f⁻¹(x) = ln(x) + 1

Answer

Setting y = e^(x−1) and solving for x: ln(y) = x − 1, so x = ln(y) + 1, giving f⁻¹(x) = ln(x) + 1.

PRE CALCULUS Practice Test