a und b werden im Potenzenbereich multipliziert,
ihre Exponenten werden addiert.
                             a und b können variiert werden.

Erklärung

Basis = 2 (slider from 2 to 10, step 0.25)
f(x) = Basis^(x)
A = Point(yAxis)
B = Point(yAxis)
g = Line(A, xAxis)
h = Line(B, xAxis)
C = Intersect(f, h, (1.5849625006771189, 2.999999999908427))
D = Intersect(f, g, (0.9999999997076958, 1.9999999995947804))
i = Line(D, yAxis)
j = Line(C, yAxis)
E = Intersect(i, xAxis)
F = Intersect(j, xAxis)
G: (x(E) + x(F), 0)
k = Line(G, yAxis)
H = Intersect(f, k, (2.5849625003848145, 5.9999999986011945))
l = Line(H, xAxis)
I = Intersect(l, yAxis)
m = Segment(B, C)
n = Segment(C, F)
p = Segment(E, D)
q = Segment(A, D)
r = Segment(I, H)
s = Segment(H, G)
Text3 = Text(x(E))
Text4 = Text(x(F))
Text5 = Text(x(G))
Text6 = Text(y(I))
Text2 = Text(("b = " * y(B)))
Text1 = Text(("a = " * y(A)))
Text7: "y = " + (LaTeX[Basis]) + "^x"
J = (0.13296259720122522, 5.665602339467803)
Text10 = VerticalText("Potenzenbereich", J)
K = (-5.88279, 10.292049935371702)
Text9 = Text("Exponentenbereich (Logarithmenbereich)")
a: y(A)
b: x(E)
c: y(B)
d: x(F)
e: x(G)
o: y(I)
Text12: "\hspace{3ex} " + (LaTeX[a]) + "=" + (LaTeX[Basis]) + "^{" + (LaTeX[b]) + "}\hspace{2ex}\\\\
\hspace{3ex} " + (LaTeX[c]) + "=" + (LaTeX[Basis]) + "^{" + (LaTeX[d]) + "}\hspace{2ex}\\\\" + (LaTeX[a]) + " \cdot " + (LaTeX[c]) + " =" + (LaTeX[Basis]) + "^{" + (LaTeX[b]) + "+" + (LaTeX[d]) + "}=  2^{" + (LaTeX[e]) + "} =" + (LaTeX[o]) + "\\\"
t = false
Text11: "\text{a} \cdot \text{b} =" + (LaTeX[o]) + ""