Solving Exponential Equations with Logarithms
Aligned to F-LE.A.4 — Common Core State Standards for Mathematics.
What this lesson teaches
To solve a × b^(ct) = d for t, first isolate the power, then take a logarithm: t = log_b(d/a) / c. A calculator evaluates the logarithm.
Worked example
Solve 5 × 2^t = 40. Divide both sides by 5 to get 2^t = 8. Then t = log_2(8) = 3, since 2^3 = 8.
Practice questions
- Solve 3^t = 81 by writing t as a logarithm.
- Solve 100 × 10^t = 100000 for t.
- Express the solution of 4 × 3^(2t) = 36 as a logarithm, then evaluate it.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Resolver ecuaciones exponenciales con logaritmos
Para resolver a × b^(ct) = d en t, primero aísla la potencia, luego aplica un logaritmo: t = log_b(d/a) / c. Una calculadora evalúa el logaritmo.
Ejemplo: Resuelve 5 × 2^t = 40. Divide ambos lados entre 5 para obtener 2^t = 8. Entonces t = log_2(8) = 3, ya que 2^3 = 8.
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