Grade 12 Logarithmic Equations Worksheet

Solve and analyze logarithmic equations, including those with different bases and properties of logarithms.

Grade 12 Math LogarithmsLogarithmic Equations

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.BF.B.5CCSS.MATH.CONTENT.HSA.REI.A.2

Topics

logarithmsequationsalgebragrade 12

7 sections · Free to use · Printable

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