Grade 12 Logarithmic Equations Worksheet
Solve and analyze logarithmic equations, including those with different bases and properties of logarithms.
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Logarithmic Equations
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Carefully read each question and solve for the unknown variable. Show all your work for full credit. Remember to check for extraneous solutions.
1. Solve for x: log₂(x) = 5
2. Solve for x: log(x + 3) = 2
3. The equation log(x) + log(x - 3) = 1 can be rewritten as a single logarithm: .
4. If ln(x) - ln(2) = ln(5), then x = .
5. Which of the following is an extraneous solution to log₄(x² - 9) - log₄(x + 3) = 1?
x = 4
x = -3
x = 7
No extraneous solutions
6. What is the solution to 2ln(x) = ln(9)?
x = 3
x = 4.5
x = 81
x = -3
7. Solve for x: log₂(x - 1) + log₂(x + 1) = 3
8. Solve for x: log₃(2x + 1) - log₃(x - 2) = 1
9. The equation log(x) = -2 has no real solution.
True
False