解对数方程 2 = log₅(3a+1) 求 a

GeoGebra 命令及参数

1. LaTeX((((("{" * Element[const1, problem]) * "}\text{a+}{") * Element[const2, problem]) * "}")) → expression
2. Sequence(x = a, a, -7, -4, 0.5) → align
3. Text("Move the slider to solve the problem.") → text0
4. LaTeX((((((("{" * Element[exponent, problem]) * "}=\log_{") * Element[base, problem]) * "}\left( {") * expression) * "}\right)")) → logeqn
5. LaTeX("y=\log_{b} {x}") → geneqn
6. LaTeX("\text{Determine values for }\textcolor{#000099}\text{b}\text{, }\textcolor{#000099}\text{x}\text{, and }\textcolor{#000099}\text{y}\text{ from the logarithmic equation.}") → text1
7. LaTeX((("\text{The general form of a logarithmic equation is }\textcolor{#000099}{" * geneqn) * "}\text{, where }\textcolor{#000099}\text{b}\text{ is the}\cr \text{base, }\textcolor{#000099}\text{x}\text{ is the argument, and }\textcolor{#000099}\text{y}\text{ is the logarithm of }\textcolor{#000099}\text{x}\text{ to the base }\textcolor{#000099}\text{b}\text{.}")) → text2
8. LaTeX("b^y=x") → genexpeqn
9. LaTeX((("\text{Write the exponential equation in the form of }\textcolor{#000099}{" * genexpeqn) * "}\text{ from the values in}\cr \text{the original problem.}")) → text4
10. LaTeX("\text{Solve the exponential equation for }\textcolor{#000099}\text{a}\text{.}") → text7
11. LaTeX((((("\text{The logarithmic equation }\textcolor{#000099}{" * geneqn) * "}\text{ is equivalent to the exponential}\cr\text{equation }\textcolor{#000099}{") * genexpeqn) * "}\text{. Therefore, substitute the determined values for }\textcolor{#000099}\text{b}\text{, }\textcolor{#000099} \text{x}\text{,}\cr\text{and }\textcolor{#000099}\text{y}\text{ into the exponential form.}")) → text5
12. LaTeX("\text{Use the buttons below to return to the original problem or}\cr \text{randomly generate a similar practice problem.}") → text11
13. LaTeX((((((("{" * Element[base, problem]) * "}^{") * Element[exponent, problem]) * "}={") * expression) * "}")) → powereqn
14. LaTeX((((("\text{The logarithmic function }\textcolor{#000099}{" * logeqn) * "}\text{ is equivalent to the}\cr\text{exponential equation }\textcolor{#000099}{") * powereqn) * "}.")) → text6
15. LaTeX((("\text{The exponential equation }\textcolor{#000099}{{" * powereqn) * "}}\text{ can be solved for }\textcolor{#000099}\text{a}\text{ using}\cr \text{algebraic techniques.}")) → text8
16. LaTeX((((("{" * Element[power, problem]) * "}={") * expression) * "}")) → sqrdpowereqn
17. LaTeX((((("{" * Element[minusconst2, problem]) * "}={") * Element[const1, problem]) * "}\text{a}")) → minuspowereqn
18. If(Element[exponent, problem] ≟ 2, LaTeX[(("\text{Square }\textcolor{#000099}{" * Element[base, problem]) * "}.")], If[Element[exponent, problem] ≟ 3, LaTeX[(("\text{Cube }\textcolor{#000099}{" * Element[base, problem]) * "}.")], If[Element[exponent, problem] ≟ 4, LaTeX[(("\text{Raise }\textcolor{#000099}{" * Element[base, problem]) * "}\text{ to the fourth power.}")], LaTeX[(("\text{Raise }\textcolor{#000099}{" * Element[base, problem]) * "}\text{ to the fifth power.}")]]]) → powerword
19. LaTeX((((("\text{In the logarithmic equation }\textcolor{#000099}{" * logeqn) * "}\text{, }\textcolor{#000099}{\text{a = }{") * Element[answer, problem]) * "}}\text{.}")) → text10
20. LaTeX((("\textcolor{#000099}{" * logeqn) * "}")) → problemtext
21. LaTeX((((((((("\text{In the function }\textcolor{#000099}{" * logeqn) * "}\text{, }\textcolor{#000099}\text{b = }\textcolor{#000099}{") * Element[base, problem]) * "}\text{, }\textcolor{#000099}\text{x = }\textcolor{#000099}{") * expression) * "}\text{, and }\textcolor{#000099}\text{y = }\textcolor{#000099}{") * Element[exponent, problem]) * "}.")) → text3
22. TableText({{LaTeX[(("\textcolor{#000099}{ {" * powereqn) * "} }")], LaTeX["Exponential \, equation"]}, {LaTeX[(("\textcolor{#000099} {" * sqrdpowereqn) * "}")], LaTeX[(("{" * powerword) * "}")]}, {LaTeX[(("\textcolor{#000099}{" * minuspowereqn) * "}")], LaTeX[(("\text{Subtract }\textcolor{#000099}{" * Element[const2, problem]) * "}\text{ from both sides.}")]}, {LaTeX[(("\textcolor{#000099}{{" * Element[answer, problem]) * "}\text{ = a}}")], LaTeX[(("\text{Divide both sides by }\textcolor{#000099}{" * Element[const1, problem]) * "}.")]}}) → text9