Express exponential solutions as logarithms

Start lessonBegins with Isolate and logarithm · Slides

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Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

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.

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

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

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