Common Core Math
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Learning Goal

Part of: Construct and compare linear, quadratic, and exponential models and solve problems — 7 of 7 cluster items

Express exponential solutions as logarithms

HSF.LE.A.4

**HSF.LE.A.4**: For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

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HSF.LE.A.4: For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

What you'll learn

  1. Isolate the exponential term in an equation of the form ab^(ct) = d by dividing both sides by a
  2. Rewrite b^(ct) = d/a in logarithmic form as ct = log_b(d/a) for b = 2, 10, or e
  3. Solve for the variable t by dividing both sides by c, obtaining t = log_b(d/a) / c
  4. Evaluate logarithmic expressions using a calculator (log for base 10, ln for base e, and the change-of-base formula for base 2)
  5. Interpret the solution in context (e.g., "the population reaches 1 million after approximately 14.2 years")
  6. Apply the logarithmic solution method to real-world exponential models involving doubling time, half-life, and target-value problems

Slides

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Slides

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