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UCSS Math III 4A.1.5 Example 1

UCSS Math III 4A.1.5 Example 1
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2014-09-15 20:28
FunctionCalculusGraphing
In collections UCSS Secondary Math III Unit 4A Lesson 1
This example demonstrates how to solve the logarithmic equation [math]\log_5 (x – 20) = 2[/math]. The core mathematical concepts involved include logarithms, logarithmic functions, and solving equations. Construction highlights: Utilizes LaTeX commands and Corner objects, step control (stepMax, stepper, steps, counter), and randomization text (RandomizationText, Original, Randomized) among other GeoGebra objects. Suitable for high school mathematics courses or teaching logarithmic functions.

GeoGebra Commands & Parameters

  1. LaTeX(steps) → counter
  2. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → RandomizationText
  3. Corner(1) → A
  4. Corner(3) → B
  5. LaTeX((((((("\textcolor{#000099}{log_{" * base) * "}(x-") * subtract) * ")=") * constant) * "}")) → text4
  6. LaTeX("\text{Simplify the left side of the equation using the fact that }\textcolor{#000099}{a^{\log_{a}(x)}=x}\text{. Simplify the}\cr\text{power on the right side of the equation.}") → text7
  7. LaTeX((("\textcolor{#000099}{x=" * Simplify[base^(constant) + subtract]) * "}")) → text10
  8. LaTeX((((((((("\text{The value of }\textcolor{#000099}{x}\text{ in the logarithmic equation }\textcolor{#000099}{\log_{" * base) * "}(x-") * subtract) * ")=") * constant) * "}\text{ is }\textcolor{#000099}{") * Simplify[base^(constant) + subtract]) * "}.")) → text11
  9. LaTeX((((((("\text{Solve for }\textcolor{#000099}{x}\text{ in the equation }\textcolor{#000099}{log_{" * base) * "}(x-") * subtract) * ")=") * constant) * "}.")) → Problem
  10. LaTeX("\text{Notice that }\textcolor{#000099}{x}\text{ is in the argument of the logarithm. In order to extract }\textcolor{#000099}{x}\text{ from the argument of any function, }\cr\text{apply the inverse of the function to both sides of the equation.") → text1
  11. LaTeX("\text{Given logarithmic equation}") → text3
  12. LaTeX("\textcolor{#000099}{y=\log_{a}(x)}") → text2_1
  13. LaTeX("\textcolor{#000099}{a^y=x}") → text2_2
  14. LaTeX((((((("\textcolor{#000099}{(" * base) * ")^{(") * constant) * ")}=(x-") * subtract) * ")}")) → text6
  15. LaTeX("\text{Solve the result for x.}") → text5_1
  16. LaTeX("\text{Rewrite in exponential form.}") → text3_1
  17. LaTeX((((((("\textcolor{#000099}{(" * base) * ")^{(") * constant) * ")}=(x-") * subtract) * ")}")) → text6_1
  18. LaTeX("\text{Exponential form of the original equation}") → text5_2
  19. LaTeX((((("\textcolor{#000099}{" * Simplify[base^(constant)]) * "=x-") * subtract) * "}")) → text8
  20. LaTeX("\text{Rewrite the equation in exponential form.}") → text5_3
  21. LaTeX("\text{Simplify.}") → text5
  22. LaTeX("\text{Move the slider to solve the problem.}") → text0
  23. LaTeX("\text{General form of a logarithmic equation}") → text3_2
  24. LaTeX("\text{A logarithmic equation of the form }\textcolor{#000099}{y=\log_{a}(x)}\text{ can be rewritten }\cr\text{as an exponential equation of the form }\textcolor{#000099}{a^y=x}.") → text2
  25. LaTeX((((((((((((("\text{The logarithmic equation }\textcolor{#000099}{log_{" * base) * "}(x-") * subtract) * ")=") * constant) * "}\text{ can be rewritten}\cr\text{as an exponential equation of the form }\textcolor{#000099}{(") * base) * ")^{(") * constant) * ")}=(x-") * subtract) * ").}")) → text2_3