指數與對數(10)
Author: 藍邦偉　老師

(1)∵|log_ax|=2011⇒\left\lbrace \begin{array}{ll} y=f(x)=|log_ax|  \  y=g(x)=2011 \ \end{array}  \right.\ 

x≥1:y=f_1(x)=-log_ax,此時f_1(x)與直線

0<x<1:y=f_2(x)=log_ax,此時f_2(x)與

故y=|log_ax|與直線y=2011交於兩點

(4)2011=log_ax_2⇒x_2=a^{2011}

(3)2011=-log_ax_1⇒a^{2011}=x_1^{-1}

$⇒x_1=\frac{1}{a^{2011}}⇒ x_1+x_2=a^{2011}+\frac{1}{a^{2011}} $

$(5) x_1·x_2=a^{2011}·\frac{1}{a^{2011}}=1 $

y=2011恰交於一點(x_1,f_1(x_1))

f_1(x)=-log_ax

直線y=2011恰交於一點(x_2,f_2(x_2))

f_2(x)=log_ax

f(x)=|log_ax|

$ (2)由(1)知，f(x)=|log_ax| 與g(x)=2011恰交$

$ 於兩點，故|log_ax|=2011恰有2相異實根 $

(x_1,f_1(x_1))

(x_2,f_2(x_2))

y=g(x)=2011

f(x) = abs(lg(x) / lg(0.5))
g(x) = -ld(x)
h(x) = -g(x)
n = 1 (slider from 1 to 11, step 1)
poly1, a, b, c, d = 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])))
poly2, e, i, j, k = Polygon(Corner[1], 0.5 * (Corner[1] + Corner[2]), 0.5 * (Corner[3] + Corner[4]), Corner[4])
A = (1.1294403110292153, 1.707176210971508)
l: y = y(A)
B = Intersect(f, l, (0.3062589241843682, 1.7071762109715094))
C = Intersect(f, l, (3.2652109711692168, 1.7071762099115333))
m = Segment(B - (0.6, 0), (x(Corner[2]), y(B)))