Algebra 2 Logarithms Test with Point Values (PDF)

Algebra 2 math test: Logarithms – Maths PDF

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This algebra 2 logarithms test for Algebra 2 covers logarithms (Common Core F-LE.A.4, F-BF.B.5, F-IF.C.7e), with a free PDF to print.

This 45-minute test on logarithms has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Logarithms
Standards: F-LE.A.4, F-BF.B.5, F-IF.C.7e
Time: 45 minutes
Total: 20 points

Algebra 2 logarithms test: questions

Question 1 – Convert forms [2 pts]

Write \(3^{4} = 81\) in logarithmic form. (1 point)
Write \(\log_{5}(125) = 3\) in exponential form. (1 point)

Question 2 – Evaluate [2 pts]

Evaluate without a calculator.

\(\log_{2}(32)\) (1 point)
\(\log_{7}(\frac{1}{7})\) (1 point)

Question 3 – Properties [3 pts]

Expand \(\log_{2}(8x^{3})\). (2 points)
Write \(\ln 6 + \ln 5\) as one logarithm. (1 point)

Question 4 – Exponential equation [3 pts]

Graphs for reference.

Solve \(4^{x} = 50\). Give the exact answer and the value to two decimal places.

Question 5 – Logarithmic equation [2 pts]

Solve \(\log_{3}(2x – 1) = 2\).

Question 6 – Change of base [2 pts]

Evaluate \(\log_{3}(40)\) to two decimal places.

Question 7 – Doubling time [2 pts]

Balance of one dollar at 4%.

An account grows at 4% per year. Solve \(1.04^{t} = 2\) for the doubling time and explain how the table agrees.

Question 8 – Graph features [2 pts]

Graph of y = log3 x.

The graph of \(y = \log_{3}(x)\) is shown. State the domain, the range, and the vertical asymptote.

Question 9 – Find the error [2 pts]

Comparison of two expressions.

Liam says \(2\log x = \log(2x)\). Use the table to show his claim is false and give the correct rewrite of \(2\log x\).

Key facts behind this algebra 2 logarithms test

Key facts

log_b(x) = y means b^y = x.
log_b(1) = 0 and log_b(b) = 1.
Product, quotient, and power rules: log(xy) = log x + log y, etc.
Change of base: log_b(x) = ln x / ln b.
The graph of log_b(x) is the reflection of b^x over y = x, with asymptote x = 0.

How to use this algebra 2 logarithms 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 Algebra 2 chapters: Algebra 2 math.

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