Montana Math MT.PLUS.ALG.EXP.5

MathGrades 9–12Exponential and Logarithmic Functions

The Standard

Solve exponential and logarithmic equations using inverse operations with and without the use of technology.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students find a missing exponent or a missing number inside a logarithm. They rewrite logarithms as powers and use calculator logarithms when an answer is not a whole number. They check that every logarithm has a positive input.
What Mastery Looks Like: A student gets x=3 for 3^(x+1)=81 and x=9 for log_2(x−1)=3, showing each inverse step. They get x≈2.81 for 2^x=7 with a calculator and check their answers.
Common Misconceptions: Some students divide 7 by 2 to solve 2^x=7 instead of using logarithms. Others turn log_2(x−1)=3 into x−1=6, or accept a value that makes a logarithm's input zero or negative.
How to Assess It: Exit ticket: Solve 3^(x+1)=81 and log_2(x−1)=3 without a calculator. Then use a calculator to solve 2^x=7 to two decimals and check each answer.

Lesson moves

Give pairs cards labeled 2^x=8, log_2(x)=3, x=3, and x=8; have them match each equation with its solution.
Ask students to explain in writing why log_2(x−1)=3 becomes x−1=8, not x−1=6.
Play two-round solve-and-check: solve 3^(x+1)=81 without a calculator, then calculate 2^x=7 to two decimals and verify by substitution.
A petri dish starts with 100 bacteria and doubles hourly; have students solve 100(2^t)=700 using calculator logarithms and check their estimate.

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