CurriculumGrade 11Mathematics

Logarithms and Exponential Equations

Aligned to F-LE.A.4 — Common Core State Standards for Mathematics.

What this lesson teaches

A logarithm answers 'what exponent is needed?' It's the inverse of an exponential, so logs solve equations where the variable is an exponent.

Worked example

Solve 2^x = 8. Since 2³ = 8, x = 3. In log form: log₂(8) = 3.

Practice questions

  1. Rewrite 10² = 100 in log form.
  2. Solve 3^x = 27.
  3. Why is a logarithm the inverse of an exponential?

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Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Logaritmos y Ecuaciones Exponenciales

Un logaritmo responde a la pregunta '¿qué exponente se necesita?' Es la operación inversa de una exponencial, por lo que los logaritmos sirven para resolver ecuaciones donde la variable es el exponente.

Ejemplo: Resuelve 2^x = 8. Como 2³ = 8, entonces x = 3. En forma logarítmica: log₂(8) = 3.

More Functions lessons

Graphing Key Features of FunctionsF-IF.C.7Equivalent Forms of a FunctionF-IF.C.8Building Functions from RelationshipsF-BF.A.1Transformations of GraphsF-BF.B.3Radian Measure of AnglesF-TF.A.1Unit Circle and Trig FunctionsF-TF.A.2

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