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UCSS Math III 4A.1.5 示例 1

UCSS Math III 4A.1.5 示例 1
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2014-09-15 20:28
函数微积分函数图像
所属专题 UCSS Secondary Math III Unit 4A Lesson 1
本范例演示了如何求解对数方程 [math]\log_5 (x – 20) = 2[/math]。涉及的核心数学概念包括对数、对数函数和等式求解。作图要点：使用了 LaTeX 命令和 Corner 对象，步骤控制（stepMax, stepper, steps, counter）以及随机化文本（RandomizationText, Original, Randomized）等 GeoGebra 对象。适合高中数学课程或对数函数的教学用途。

GeoGebra 命令及参数

  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