Montana Math MT.PLUS.ALG.EXP.3.b
The Standard
- MT.PLUS.ALG.EXP.3
- Understand that exponential and logarithmic functions can be represented using multiple forms by: Expressing exponential functions in the form f(x) = a · b^x and f(x) = Pe^(r·t), and Expressing logarithmic functions in base 10 and base e.
Understand that exponential and logarithmic functions can be represented using multiple forms by: Expressing logarithmic functions in base 10 and base e.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite a logarithm using base 10 or base e. They use either form to find its value on a calculator.
What Mastery Looks Like
- Given log₂(8), a student writes log(8)/log(2) and ln(8)/ln(2). They get 3 from either form and explain why the denominator uses the original base.
Common Misconceptions
- Students may treat log(x) and ln(x) as the same function, or think ln(8) alone equals log₂(8). Some reverse the numerator and denominator when changing bases.
How to Assess It
- On an exit ticket, ask students to rewrite log₄(64) using both log and ln, then evaluate it. Look for log(64)/log(4) = ln(64)/ln(4) = 3.
Lesson moves
Ways to Teach It
Give pairs cards marked log₄(64), log(64)/log(4), ln(64)/ln(4), and 3; have them group equal values.
Ask students to write two sentences explaining why ln(8) alone does not equal log₂(8).
Run a whiteboard relay with log₅(125), log₃(81), and log₂(16); teams write both change-of-base forms.
A bacteria count doubles to eight times its starting size; have students find the number of doublings with log(8)/log(2) and ln(8)/ln(2).
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Related Standards
- MT.PLUS.ALG.EXP.3
Understand that exponential and logarithmic functions can be represented using multiple forms by: Expressing exponential functions in the form f(x) = a · b^x an...
- MT.PLUS.ALG.EXP.3.a
Expressing exponential functions in the form f(x) = a · b^x and f(x) = Pe^(r·t), and
- MT.PLUS.ALG.EXP.4
Graph logarithmic and exponential functions with and without the use of technology by identifying intercepts, asymptotes, and end behavior.
- MT.PLUS.ALG.EXP.1
Understand logarithmic functions as the inverse of exponential functions.
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