指數與對數(4)
Author: 藍邦偉　老師

(1)\sqrt{\sqrt{\frac{1}{3}}}=\sqrt[4]{\frac{1}{3}}=3^{-\frac{1}{4}}=3^{-0.25}

(2)\frac{3^{\sqrt{3}}}{9}=\frac{3^{\sqrt{3}}}{3^2}=3^{\sqrt{3}-2}≈3^{-0.268}

(3)\sqrt[4]{\frac{1}{27}}=3^{-\frac{3}{4}}=3^{-0.75}

$ (4)(\sqrt[3]{3^8})^{-0.25}=(3^{\frac{8}{3}})^{-\frac{1}{4}} =3^{-\frac{2}{3}}≈3^{-0.67}$

(5)\frac{1}{(\sqrt[6]{3})^2}=\frac{1}{3^{\frac{2}{6}}}=3^{-\frac{1}{3}}≈3^{-0.33}

∵-0.75<-0.67<-0.33<-0.268<-0.25

∴3^{-0.75}<3^{-0.67}<3^{-0.33}<3^{-0.268}<3^{-0.25}

$ ∴\sqrt[4]{\frac{1}{27}} 最小$

y=3^x

-0.75

-0.67

-0.33

      $ ↓$
$-0.27$

-0.25

n = 1 (slider from 1 to 10, step 1)
f(x) = 3^(x)
C: (-0.33, f(-0.33))
B: (-0.67, f(-0.67))
A: (-0.75, f(-0.75))
D: (-0.27, f(-0.27))
E: (-0.25, f(-0.25))
A_1: (x(A), 0)
B_1: (x(B), 0)
C_1: (x(C), 0)
D_1: (x(D), 0)
E_1: (x(E), 0)
a = Segment(A, A_1)
b = Segment(B, B_1)
c = Segment(C, C_1)
d = Segment(D, D_1)
e = Segment(E, E_1)
poly1, g, h, i, j = Polygon(Corner[1], Corner[2], Corner[3], Corner[4])
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))