Free Printable WorksheetMathAlgebra IIMath CurriculumALG2.169

ALG2.169 Change of Base and Calculator Use Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.169 Change of Base and Calculator Use. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.169 Change of Base and Calculator Use - Practice questions for Change of Base and Calculator Use.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.169 Change of Base and Calculator Use skill assessments:

Problem 1Difficulty: Mastery

Which reasoning correctly explains why log₂(7) is greater than log₃(7)?

ABecause 2 is greater than 3.

BBecause 7 is a prime number.

CBecause a smaller base always makes the log value smaller.

DBecause log_b(7)=ln(7) ÷ ln(b), and ln(2) is smaller than ln(3), so dividing by ln(2) gives a larger value.

Solution & Explanation:Using change-of-base, log₂(7)=ln(7) ÷ ln(2) and log₃(7)=ln(7) ÷ ln(3). The numerator is the same and ln(2)

Problem 2Difficulty: Mastery

Solve for x: logₓ(16)=log₂(3). Round x to the nearest thousandth.

Solution & Explanation:Change-of-base: ln(16) ÷ ln(x)=ln(3) ÷ ln(2). So ln(x)=(ln(16)·ln(2)) ÷ ln(3), and x=e raised to ((ln(16)·ln(2)) ÷ ln(3))≈5.751.

Problem 3Difficulty: Mastery

Suppose log_b(50)=log₅(2). Which expression correctly gives b?

Ab=50 raised to (log₅(2))

Bb=5 raised to (log₅(2) ÷ 50)

Cb=e raised to ((ln(50)·ln(5)) ÷ ln(2))

Db=ln(50) ÷ ln(2)

Solution & Explanation:Set ln(50) ÷ ln(b)=ln(2) ÷ ln(5). Cross-multiply: ln(b)=(ln(50)·ln(5)) ÷ ln(2), so b=e raised to ((ln(50)·ln(5)) ÷ ln(2)).

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard ALG2.169 (Practice questions for Change of Base and Calculator Use.).