Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a logarithms test PDF? Then this Algebra 2 test on Logarithms: The Inverse of Exponents checks the whole chapter, with points for each question. This 45-minute test covers converting forms, evaluating logarithms, graphs, expanding and condensing, change of base, and scale applications. A scientific calculator is allowed. Show every step of the work for full credit.
Standards: F-LE.A.4, F-BF.B.4a, F-IF.C.7e · Level: Grade 11 Algebra 2
Question 1 Convert between forms (2 points)
- Write 72 = 49 in logarithmic form. (1 point)
- Write log10 0.01 = −2 in exponential form. (1 point)
Question 2 Evaluate logarithms (3 points)
Evaluate each logarithm without a calculator.
- log4 64 (1 point)
- log9 3 (1 point)
- ln e7 + log 1000 (1 point)
Question 3 Read a logarithmic graph (3 points)
The graph shows a function of the form y = log2(x + 2) − 1.
- State the equation of the vertical asymptote. (1 point)
- State the domain. (1 point)
- Verify algebraically that (6, 2) lies on the graph. (1 point)
Question 4 Expand a logarithm (2 points)
Expand log2(8p2q) completely.
Question 5 Condense and simplify (2 points)
Write log6 12 + log6 3 as a single logarithm and evaluate it.
Question 6 Change of base (2 points)
Approximate log7 90 to the nearest hundredth.
Question 7 pH of a solution (2 points)
A solution has [H+] = 4 × 10−9 moles per liter. Find its pH to the nearest hundredth. Is it acidic or basic?
Question 8 Inverse from a graph (2 points)
The graph shows y = 2x. Write the coordinates of three points on the inverse function and its equation.
Question 9 Decibels (2 points)
Use L = 10 log(I/I0) with I0 = 10−12 W/m². Find L for I = 8 × 10−6 W/m², to the nearest tenth.
