指數函數與對數函數的對稱
Author: 藍邦偉  老師

x

y

y=x

x

指數函數與對數函數的對稱

a = 2 (slider from 0 to 10, step 0.1)
f(x) = log(x) / log(a)
A = Corner(1)
B = Corner(3)
C: (x(A), 0)
D: (x(B), 0)
u = Vector(C, D)
E: (0, y(A))
F: (0, y(B))
v = Vector(E, F)
S = Intersect(s, t)
g(x) = a^(x)
b = 0 (slider from 0 to 20, step 0.01)
G: (b, f(b))
d = OrthogonalLine(G, c)
H = Intersect(g, d, (3.876762490407144, 14.689999996187622))
I = Intersect(c, d)
e = Segment(H, I)
h = Segment(I, G)
text1: "y=" + a + "^x"
text2: "y=log_{" + (LaTeX[a]) + "}x"

Tool: 2D-AXIS (command 工具1)
2D-Axis
Input: A, B, C, D, E, F
Output: u, v

x

y

C: (x(A), 0)
D: (x(B), 0)
u = Vector(C, D)
E: (0, y(A))
v = Vector(E, F)