Exponentialgleichung
a und b können variiert werden.

Erläuterung

grafisch Dividieren (Strahlensatz)

Basis = 2 (slider from 2 to 10, step 0.25)
f(x) = Basis^(x)
B = Point(yAxis)
A = Point(yAxis)
g = Line(B, xAxis)
h = Line(A, xAxis)
C = Intersect(f, h, (2.0147283947228583, 4.0410449373816615))
D = Intersect(f, g, (3, 8))
i = Line(D, yAxis)
j = Line(C, yAxis)
E = Intersect(i, xAxis)
F = Intersect(j, xAxis)
m = Segment(A, C)
n = Segment(C, F)
p = Segment(E, D)
q = Segment(B, D)
Text3 = Text(x(E))
Text4 = Text(x(F))
Text7: "y = " + (LaTeX[Basis]) + "^x"
J = (0.13296259720122522, 5.665602339467803)
Text10 = VerticalText("Potenzenbereich", J)
K = (-5.88279, 10.292049935371702)
Text9 = Text("Exponentenbereich (Logarithmenbereich)")
xx: x(E) / x(F)
d: x(F)
e: x(E)
Text5: "x = \frac{" + (LaTeX[e]) + "}{" + (LaTeX[d]) + "}\\\\\\
\hspace{2ex}=" + (LaTeX[xx]) + ""
b: y(B)
k: y(A)
Text2 = Text(("a = " * y(A)))
Text1 = Text(("b = " * y(B)))
Text8: "
a^x=b  \\\\\\" + (LaTeX[k]) + "^x=" + (LaTeX[b]) + "
                         "
Text6: "\hspace{7ex} " + (LaTeX[k]) + "^x=" + (LaTeX[b]) + "\\\\\\
\hspace{8ex} " + (LaTeX[k]) + "=" + (LaTeX[Basis]) + "^{" + (LaTeX[d]) + "}\hspace{2ex}\\\\
\hspace{8ex} " + (LaTeX[b]) + "=" + (LaTeX[Basis]) + "^{" + (LaTeX[e]) + "}\\\\
\hspace{4ex} \big ( " + (LaTeX[Basis]) + "^{" + (LaTeX[d]) + "}\big)^x=" + (LaTeX[Basis]) + "^{" + (LaTeX[e]) + "}\\
\hspace{5ex} " + (LaTeX[d]) + "\cdot x = " + (LaTeX[e]) + "\\\\\\
\hspace{8ex} x=" + (LaTeX[xx]) + ""
a = false
G = Intersect(f, yAxis, (0, 1))
l = Segment(F, G)
r = Line(E, l)
H = Intersect(r, yAxis)
s = Segment(H, E)
c: y(H)
Text12: "x = " + c + ""
o = false