Exponential and Logarithmic Equations Test – Algebra 2 Math (Printable PDF)

Question 1 Same-base equation (2 points)

Solve 3^x−2 = 81.

Question 2 Exponential equation (2 points)

Solve 6^x = 50. Round to the nearest hundredth.

Question 3 Isolate and solve with e (2 points)

Solve 4e^0.5x = 30. Round to the nearest hundredth.

Question 4 Logarithmic equation (2 points)

Solve log₇(2x + 3) = 2.

Question 5 Equation with two logarithms (3 points)

Solve log₅ x + log₅(x + 4) = 1. Check for extraneous solutions.

Question 6 Decay model (3 points)

The graph shows y = 100(0.8)^x, the percent of a charge left after x hours.

1. Estimate from the graph when 40 percent remains. (1 point)
2. Find the exact time using logarithms. (2 points)

Question 7 Compound interest (2 points)

Dara invests $2,500 at 3.8% interest compounded monthly. How many years until the account holds $4,000? Round to the nearest tenth.

Question 8 Half-life (2 points)

A medicine has a half-life of 5 hours and the initial dose is 200 mg. After how many hours is 25 mg left?

Question 9 Extraneous solution (2 points)

Solve log x + log(x + 9) = 1 and explain why one of the two algebraic solutions is rejected.