Exponential and Logarithmic Equations Worksheet

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

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Looking for an exponential and logarithmic equations worksheet PDF? Then this Algebra 2 worksheet on Using Logs to Solve Exponent Equations gives problems ranked from easy to hard. These problems train solving equations with the unknown in an exponent or inside a logarithm, standards F-LE.A.4 and A-SSE.B.3c.

They begin with matching bases, move to logarithm methods and extraneous roots, and finish with interest, half-life, population, pH and sound-level applications.

Standards: F-LE.A.4, A-SSE.B.3c · Level: Grade 11 Algebra 2

Sommaire

Problem 1 Match the bases ★★★

Solve 3^x = 729.

Problem 2 Same base on both sides ★★★

Solve 4^x+1 = 64.

Problem 3 Simplest logarithmic equation ★★★

Solve log₅ x = 3.

Problem 4 Negative log value ★★★

Solve log₂ x = −3.

Problem 5 Isolate, then match bases ★★★

Solve 3 · 2^x = 48.

Problem 6 Exponential equation with logs ★★★

Solve 7^x = 20. Round to the nearest hundredth.

Problem 7 Base e equation ★★★

Solve e^2x = 15. Round to the nearest hundredth.

Problem 8 Logarithm with a shifted argument ★★★

Solve log(x + 4) = 2.

Problem 9 Graph of an exponential equation ★★★

The graph shows y = 3 · 2^x and the line y = 45. Solve 3 · 2^x = 45 exactly, then to the nearest hundredth.

Graph of y = 3 · 2^x and y = 45.

Problem 10 Natural log on a graph ★★★

The graph shows y = ln x and the line y = 2. Find the exact x-coordinate of the intersection and approximate it to the nearest hundredth.

Graph of y = ln x and y = 2.

Problem 11 Condense logs and solve ★★★

Solve ln x + ln(x + 2) = ln 24. Reject any extraneous solution.

Problem 12 Different bases on each side ★★★

Solve 2^x+3 = 5^x. Round to the nearest hundredth.

Problem 13 Logarithm equation leading to a quadratic ★★★

Solve log x + log(x − 3) = 1.

Problem 14 Equation with a coefficient on the log ★★★

Solve 3 log₂(x − 1) + 5 = 14.

Problem 15 Savings goal with annual compounding ★★★

Camille deposits $6,000 in an account paying 4.5% interest compounded annually. After how many years will the balance reach $9,000? Round to the nearest hundredth of a year.

Balance of the account over 12 years.

Problem 16 Medicine half-life ★★★

A 80 mg dose of a medicine has a half-life of 6 days, so the amount left is A(t) = 80(1/2)^t/6. After how many days does 15 mg remain? Round to the nearest tenth.

Medicine remaining over 30 days.

Problem 17 Town population growth ★★★

The population of a town is modeled by P = 1200e^0.035t, where t is years since 2020. When will the population reach 2,000? Give the year, rounding up to the next whole year.

Problem 18 Doubling time at 3.2% ★★★

An investment grows continuously at 3.2% per year, A = Pe^0.032t. Find the doubling time to the nearest tenth of a year, and explain why the starting amount P does not matter.

Problem 19 Hydrogen ion concentration ★★★

Black coffee has a pH of 4.3. Use pH = −log[H⁺] to find [H⁺] in scientific notation with the coefficient rounded to the nearest hundredth.

Problem 20 Comparing two sound levels ★★★

A concert is 92 dB and a conversation is 68 dB, where L = 10 log(I/I₀). How many times greater is the intensity of the concert? Round to the nearest whole number.

Exponential And Logarithmic Equations lesson Exponential And Logarithmic Equations test Exponential And Logarithmic Equations quiz

Mis à jour le 22 October 2026