Grade 11 · Math · Algebra 2

11th grade Solve logarithmic equations worksheet

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Solve logarithmic equations

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Pia joins the logs to solve log₅ x + log₅ 8 − log₅ 2 = 2. What is x?
Tala joins the logs to solve log₃ x + 2 log₃ 5 = 4. What is x?
Zee solves ln x = 2.5 with a calculator. To the nearest hundredth, what is x?
Bo solves ln (x + 1) = 3 with a calculator. To the nearest hundredth, what is x?
Esme solves ln (2x) = 4 with a calculator. To the nearest hundredth, what is x?
Jun solves log (x − 3) = 1.5 with a calculator. To the nearest hundredth, what is x?
7.
Kira solves 2 log₃ x = log₃ (x + 6) on a math club card. Which choice gives every solution?
- no solution
- x = 3 only
- x = -2 only
- x = 3 and x = -2
8.
Luz solves log₂ (x² + 12) − log₂ x = 3 on a math club card. Which choice gives every solution?
- x = 2 only
- x = 2 and x = 6
- no solution
- x = 6 only
9.
Noah solves log₃ (x² + 18) − log₃ x = 2 on a math club card. Which choice gives every solution?
- no solution
- x = 3 only
- x = 6 only
- x = 3 and x = 6
10.
Pia solves log₂ (x − 1) − log₂ (x + 3) = 1 on a math club card. Which choice gives every solution?
- no solution
- x = 7 only
- x = -7 only

Logarithmic equations. Every version has 10 questions, and the answer key prints on the second page.

I can rewrite log_b X = c as X = b^c and solve for x.
I can join logs with one base into one log, or set two insides equal, and solve.
I can check every answer in the first equation and keep only the ones whose insides are above 0.

Standard: A-REI.A.1 (related)

logarithmic equation: An equation with x inside a log.

rewrite: Turn log_b X = c into X = b^c: X sits in row c.

inside (argument): The number or expression a log is taken of; it must be above 0.

condense: Join several logs with one base into one log.

fake answer (extraneous): An answer of the equation without logs that fails in the first equation.

check: Put the answer back into every log and make sure each inside is above 0.

Rewrote log₂ x = 5 as x = 5² instead of x = 2⁵. Read it aloud together: "2 to the 5th power is x."

Multiplied the base by the number (2 × 5) instead of raising it (2⁵). Write 2⁵ as 2 × 2 × 2 × 2 × 2 together.

Moved a number across the equals sign with the wrong sign.

Ask: to undo + 3, do you add or subtract 3?

What is the most common mistake with solve logarithmic equations?

Rewrote log₂ x = 5 as x = 5² instead of x = 2⁵. Read it aloud together: "2 to the 5th power is x."

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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