求解指数方程示例 by Walch Education

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((("\text{Add }\textcolor{#000099}{" * subtract) * "}\text{ to both sides.}")) → text9
6. LaTeX((((((("\text{Solve for }\textcolor{#000099}{x}\text{ in the equation }\textcolor{#000099}{" * base) * "^{x-") * subtract) * "}=") * constant) * "}.")) → Problem
7. LaTeX("\text{Notice that }\textcolor{#000099}{x}\text{ is in the exponent. In order to extract }\textcolor{#000099}{x}\text{ from the}\cr\text{argument of any function, apply the inverse of the function to both sides of the}\cr\text{equation.") → text1
8. LaTeX((((((("\textcolor{#000099}{" * base) * "^{x-") * subtract) * "}=") * constant) * "}")) → text4
9. LaTeX((("\text{Take the logarithm base }\textcolor{#000099}{" * base) * "}\text{ both sides.}")) → text5
10. LaTeX((((((((((("\textcolor{#000099}{log_{" * base) * "}\left(") * base) * "^{x-") * subtract) * "}\right)=log_{") * base) * "}(") * constant) * ")}")) → text6
11. LaTeX((("\textcolor{#000099}{x\approx" * finalans) * "}")) → text10
12. LaTeX((((((((("\text{The value of }\textcolor{#000099}{x}\text{ in the exponential equation }\textcolor{#000099}{" * base) * "^{x-") * subtract) * "}=") * constant) * "}\text{ is approximately }\textcolor{#000099}{") * finalans) * "}.")) → text11
13. LaTeX("\textcolor{#000099}{y=a^x}") → text2_1
14. LaTeX("\text{General form of an exponential equation}") → text3_1
15. LaTeX("\textcolor{#000099}{\log_{a}(y)=x}") → text2_2
16. LaTeX("\text{Rewrite in logarithmic form.}") → text3_2
17. LaTeX("\text{Given exponential equation}") → text3
18. LaTeX((((((("\textcolor{#000099}{\log_{(" * base) * ")}(") * constant) * ")=(x-") * subtract) * ")}")) → text2_3
19. LaTeX("\text{Substitute.}") → text3_3
20. LaTeX((((((("\textcolor{#000099}{\log_{(" * base) * ")}(") * constant) * ")=(x-") * subtract) * ")}")) → text2_5
21. LaTeX("\text{Logarithmic form of the original equation}") → text3_4
22. LaTeX((((("\textcolor{#000099}{(" * ans) * ")\approx x-") * subtract) * "}")) → text8
23. LaTeX("\text{Move the slider to solve the problem.}") → text0
24. LaTeX("\text{An exponential equation of the form }\textcolor{#000099}{y=a^x}\text{ can be rewritten }\cr\text{as a logarithmic equation of the form }\textcolor{#000099}{\log_{a}(y)=x}.") → text2
25. LaTeX((((((((((((("\text{The exponential equation }\textcolor{#000099}{" * base) * "^{x-") * subtract) * "}=") * constant) * "}\text{ can be rewritten as the }\cr\text{logarithmic equation }\textcolor{#000099}{\log_{(") * base) * ")}(") * constant) * ")=(x-") * subtract) * ")}.")) → text2_4
26. LaTeX("\text{Find the common logarithm with}\cr\text{a calculator and substitute.}") → text7