AP® Precalculus – Exponential and Logarithmic Equations – Drill 19

About This Drill

AP® Precalculus – Exponential and Logarithmic Equations – Drill 19 is a Math practice drill covering Exponential and Logarithmic Equations. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

This AP(r) Precalculus drill covers solving exponential and logarithmic equations (Topics 2.13-2.14), including converting between forms, applying logarithm properties, and solving equations in real-world contexts. Master these algebraic techniques to handle a wide range of exam problems.

Questions in This Drill

1. Which value of \( x \) satisfies the equation \( 2^{3x-1} = 32 \)?
2. Which value of \( x \) satisfies the equation \( \log_3(2x + 3) = 3 \)?
3. A population of bacteria is modeled by \( P(t) = 500 \cdot 2^{t/4} \), where \( t \) is time in hours. After how many hours will the population equal 8,000?
4. Which value of \( x \) satisfies \( \log_2 x + \log_2(x - 6) = 4 \)?
5. The concentration of a substance decays according to \( C(t) = C_0 \cdot e^{-kt} \). Measurements show that \( C(2) = 80 \) and \( C(5) = 20 \). Which of the following is the value of the decay constant \( k \)?