对数方程求解示例：解方程log_5(x-20)=2

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