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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students isolate the exponential factor, rewrite the unknown exponent using a logarithm, and solve for the variable. They use base-2 log, common log, or natural log as appropriate, then evaluate with a calculator.
What Mastery Looks Like
- A student isolates the exponential expression before taking a logarithm. They write t = log_b(d/a)/c, or an equivalent change-of-base form, and calculate an accurate decimal. They check the result by substitution and include reasonable units when needed.
Common Misconceptions
- Students may take the logarithm before dividing by the coefficient, or treat log(d/a) as log d divided by log a. Some solve for ct but forget to divide by c. Others confuse common log with natural log or omit calculator parentheses.
How to Assess It
- Exit ticket: Solve 5·2^(0.3t) = 47, write a logarithmic expression, and round t to the nearest tenth. The result should be about 10.8.
Lesson moves
Ways to Teach It
Give pairs doubling-time and target-value cards; students build a table, estimate t, then use logarithms to refine the estimate.
Post two solutions to 3·2^(0.4t) = 25, one dividing by 3 first, and ask students to defend the valid method.
Run a card sort matching exponential equations, isolated exponential forms, logarithmic expressions, and calculator answers.
Use A = 120e^(-0.18t) for medicine in the body, and have students find when 30 milligrams remain.
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Printable HSF-LE.A.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-LE.A.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSF-BF.B.5
Solving exponential model equations by writing logarithms directly requires knowing logarithms undo exponents.
- CCSS.Math.Content.HSA-SSE.B.3c
Rewriting exponential expressions supports isolating and interpreting b^(ct) before using logarithms to solve for the exponent.
- CCSS.Math.Content.HSA-CED.A.4
Solving the exponential equation requires isolating the exponential term and the variable before applying a logarithm.
Keep exploring
Related Standards
- 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
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