Logarithmic Equations Worksheet

This worksheet provides practice with solving various types of logarithmic equations, including those with different bases and requiring the use of logarithmic properties.

Grade 11 Math LogarithmsLogarithmic Equations

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Includes

2 Short AnswerFill in the BlanksMultiple Choice

Standards

CCSS.MATH.CONTENT.HSF.BF.B.5CCSS.MATH.CONTENT.HSF.LE.A.4

6 sections · Free to use · Printable

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Logarithmic Equations Practice

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Solve each logarithmic equation. Show all your work. Remember to check for extraneous solutions.

1. Solve for x: log₂(x) = 5

2. Solve for x: log₃(x - 2) = 4

3. If log(x) + log(x + 3) = 1, then x = .

4. The solution to log₅(x + 6) - log₅(x) = 2 is x = .

5. Which of the following is the solution to ln(x) = 3?

x = 3e

x = e³

x = ln(3)

x = 3/e

6. What is the value of x in the equation log₂(x) + log₂(x - 7) = 3?

x = 1

x = 8

x = -1

x = 8 and x = -1

7. Solve for x: log(x + 2) + log(x - 1) = 1 (Remember to check for extraneous solutions).

8. Solve for x: ln(e^(2x) - 3) = ln(e^x) + ln(2)