CCSS.Math.Content.HSF-LE.A.4
The standard
For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Common Core State Standards for Mathematics
What this standard means
Students need to solve exponential equations where the variable is in the exponent. They should isolate the exponential part, rewrite the equation as a logarithm, and use a calculator or graphing tool to evaluate it. Bases are limited to 2, 10, and e.
Mastery means students can move from an equation like 3·2^(0.4t)=18 to 2^(0.4t)=6, then 0.4t=log₂(6), then calculate t. Common trouble spots are forgetting to divide by the coefficient first, mixing up the base of the log, and rounding too early.
Ways to teach it
- Hands-on: Give pairs equation cards and calculator cards, then have them match each exponential equation to its logarithmic solution and decimal answer.
- Prompt: Explain why 5·10^(2t)=80 cannot become 2t=log(80) before doing any other step.
- Quick assessment: Ask students to solve 7e^(0.3t)=42 and write one sentence naming each step they used.
- Real-world connection: Use a bacteria growth equation and ask students to find when the population reaches a stated lab safety limit.
Plan a lesson for CCSS.Math.Content.HSF-LE.A.4
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Related standards
- CCSS.Math.Content.HSF-BF.B.5
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
- CCSS.Math.Content.HSF-LE.A.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
- CCSS.Math.Content.HSF-LE.B.5
Interpret the parameters in a linear or exponential function in terms of a context.
- CCSS.Math.Content.HSF-LE.A
Construct and compare linear, quadratic, and exponential models and solve problems