Grade 11Algebraic ThinkingOriginal practice

Logarithms Laws Domains and Valid Equations: Explore and Explain Worksheet — Grade 11

Logarithms Laws Domains and Valid Equations: Explore and Explain: Interpret a logarithm as the inverse of an exponential rule. Starts with 2 practice tasks. Answer guidance included. Print on Letter/A4 or save as PDF from the print window.

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Independent activity · About 12 minutes · Pencil · Algebra 2

Practice set 1 of 3. Each set keeps the same learning goal and task structures.

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Grade 11 · Mathematics

Logarithms Laws Domains and Valid Equations: Explore and Explain

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Grade 11 · Mathematics · continued

Logarithms Laws Domains and Valid Equations: Explore and Explain

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Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Worked example: log₄(16)=2 because 4²=16. For positive u and v, log₄(u)+log₄(v)=log₄(uv); adding the arguments is a different operation. Explore the material. Talk through your reasoning with suitable support.

1.Evaluate log_2(8).

2.Rewrite log_2(y) = 3 in exponential form and find y.

Grade 11 · Mathematics · Answer key

Logarithms Laws Domains and Valid Equations: Explore and Explain

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Grade 11 · Mathematics · Answer key · continued

Logarithms Laws Domains and Valid Equations: Explore and Explain

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Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

1.Evaluate log_2(8).

Answer:3

2.Rewrite log_2(y) = 3 in exponential form and find y.

Answer:2^3 = y; y = 8

About this practice

Grade 11 · Mathematics · Matching answer key included · US Letter and A4

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Teaching guide, sample answers and curriculum references

Before you begin

Use positive-base powers, inverse functions, factoring and original-equation domain checks.

How to use this worksheet

Begin with: Evaluate log_2(8).
Connect the response to: State the real domain for the two logarithms in the material.
Ask students to apply the idea: A learner writes log_2(u) + log_2(v) = log_2(u + v). Correct this for positive u and v. Check using u = v = 2.

A common mistake to discuss

A condensed logarithm can hide invalid original arguments; base 1 cannot define a logarithm.

What to practice next

Continue to Logarithms Laws Domains and Valid Equations: Practice Independently.

Original instructional material written for this practice.

Source reference: Selected high-school course targets.

Published 2026-10-08; updated 2026-10-08. Read our editorial policy.

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Logarithms Laws Domains and Valid Equations

Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Worked example: log₄(16)=2 because 4²=16. For positive u and v, log₄(u)+log₄(v)=log₄(uv); adding the arguments is a different operation. Use the material to work through each task. Show the requested response.

1.Evaluate log_2(8).

Practice preview

Grade 11

Key

Logarithms Laws Domains and Valid Equations

Practice · Independent · 45 min

Interpret a logarithm as the inverse of an exponential rule. Apply product laws and solve with positive-argument restrictions. Explain invalid laws, extraneous roots and base conditions. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Logarithms Laws Domains and Valid Equations: Apply and Create

Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Use what you learned to explain, construct or apply an idea.

1.A learner writes log_2(u) + log_2(v) = log_2(u + v). Correct this for positive u and v. Check using u = v = 2.

Practice preview

Grade 11

Key

Logarithms Laws Domains and Valid Equations: Apply and Create

Apply · Independent · 25 min

Interpret a logarithm as the inverse of an exponential rule. Apply product laws and solve with positive-argument restrictions. Explain invalid laws, extraneous roots and base conditions. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

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Logarithms Laws Domains and Valid Equations: Practice Independently

Logarithms reverse positive powers

Use base 2. For positive y, log_2(y) = x means 2^x = y. Consider log_2(x − 1) + log_2(x + 1) = 3. Both logarithm arguments must be positive. Apply a law only on its valid domain.

Use the material to work through each task. Show the requested response.

1.State the real domain for the two logarithms in the material.

Practice preview

Grade 11

Key

Logarithms Laws Domains and Valid Equations: Practice Independently

Practice · Independent · 20 min

Interpret a logarithm as the inverse of an exponential rule. Apply product laws and solve with positive-argument restrictions. Explain invalid laws, extraneous roots and base conditions. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

Preview / Print →

Practice preview

Grade 11

HSF.LE.A.4 Key

Algebra 2: Exponential & Logarithmic Functions

Practice · Independent · 35 min

Selected high-school practice with evidence, conditions and a written explanation.

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