對數內插求值
Author: 藍邦偉  老師

$ O $

$ f(x)=log\;x $

$ x $

$ 對數內插求值 $

set1

$ 1：\;1 $

$ 放大\;y\;軸單位長$

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.72 * Corner[1] + 0.28 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
f(x) = log(10, x)
A = Point(Segment[(1, 0), (10, 0)])
List_1 = Sequence((k, f(k)), k, 1, 10)
List_2 = Sequence(Segment[Element[List_1, k], (k, 0)], k, 1, 10, 1)
List_3 = Sequence(Segment[(0, lg(k)), Element[List_1, k]], k, 1, 10)
B: (x(A), f(x(A)))
a_1 = Segment(B, A)
C: (0, y(B))
b = Segment(C, B)
text2: "$ " + (LaTeX[y(C)]) + " $"
Sol1: "$∵ " + (LaTeX[lg(floor(x(A)))]) + "≤" + (LaTeX[y(C)]) + "≤" + (LaTeX[lg(floor(x(A)) + 1)]) + " $
$⇒log\;" + (LaTeX[floor(x(A))]) + "≤log\;x≤log\;" + (LaTeX[floor(x(A)) + 1]) + "$"
Ans: "$⇒ \frac{x-" + (LaTeX[floor(x(A))]) + "}{" + (LaTeX[floor(x(A)) + 1]) + "-" + (LaTeX[floor(x(A))]) + "}=\frac{" + (LaTeX[y(C)]) + "-" + (LaTeX[f(floor(x(A)))]) + "}{" + (LaTeX[f(floor(x(A)) + 1)]) + "-" + (LaTeX[f(floor(x(A)))]) + "} $
$⇒x=" + (LaTeX[floor(x(A))]) + "+\frac{" + (LaTeX[y(C) - f(floor(x(A)))]) + "}{" + (LaTeX[f(floor(x(A)) + 1) - f(floor(x(A)))]) + "}×1$
$\;\;\;\;\;\;\;=" + (LaTeX[x(A)]) + "$
$∴log" + (LaTeX[x(A)]) + "=" + (LaTeX[y(C)]) + "$"
Question: "$ log\;x=" + (LaTeX[y(C)]) + " ,\;x=?$
$Sol：$"
c = false
d = true