Precalculus Exponential and Logarithmic Equations Test with Point Values (PDF)
This exp log equations test for Precalculus covers exponential and logarithmic equations (Common Core F-LE.A.4, F-BF.B.5, A-REI.D.11), with a free PDF to print.
Time and points
- Grade: Precalculus
- Chapter: Exponential and Logarithmic Equations
- Standards: F-LE.A.4, F-BF.B.5, A-REI.D.11
- Time: 45 minutes
- Total: 20 points
Exp log equations test: questions
Question 1 – Exponential equations [2 pts]
Solve (a) \(3^{x+2}=81\); (b) \(7^{x}=50\) to three decimal places.
Question 2 – Base e equation [2 pts]
Solve \(e^{3x}=20\) to three decimal places.
Question 3 – Isolate the power [2 pts]
Solve \(5\cdot2^{x}=70\) to three decimal places.
Question 4 – Log equation [2 pts]
Solve \(\log_{3}(2x-1)=2\).
Question 5 – Combine and check [3 pts]
Solve \(\log x+\log(x+3)=1\). (a) Combine the logarithms. (b) Solve the resulting equation. (c) Check each solution.
Question 6 – Two logs equal [2 pts]
Solve \(\ln x+\ln(x-2)=\ln15\).
Question 7 – Savings goal [2 pts]
How long will it take \(\$2{,}500\) at \(4\%\) compounded yearly to grow to \(\$4{,}000\)? Give the answer to the nearest hundredth.
Question 8 – Radioactive decay [3 pts]
A sample decays by \(A(t)=800e^{-0.05t}\) grams after \(t\) days. (a) Find \(A(10)\) to the nearest tenth. (b) When does the mass reach \(400\) g? (c) When does it reach \(100\) g? Give answers to the nearest hundredth.
Question 9 – Different bases [2 pts]
Solve \(3^{x-1}=2^{x}\) to three decimal places.
Key facts behind this exp log equations test
- Same base: if b^m = b^n then m = n.
- Different bases: take ln of both sides, then x ln b = ln c.
- log_b u = c is equivalent to u = b^c.
- Check log solutions: arguments must be positive; reject extraneous values.
- Continuous doubling time is ln 2 divided by the rate r.
How to use this exp log equations test
Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.
All Precalculus chapters: Precalculus math.
Free printable PDF
