常用對數的近似值
Author: 藍邦偉老師

$ 常用對數的近似值 $

$ x $

r = 0.6 (slider from 0.1 to 0.9, step 0.1)
List_1 = Sequence(Segment[(-4, k), (14, k)], k, -10, 10)
J = Point(List_1)
R = (2.634742857142852, 0.22617142857143344)
a_7 = Ray(R, J)
c_a = Circle(R, r)
K = Intersect(c_a, a_7)
f(x) = lg(x)
O = (-5, -4)
d_a = Circle(O, 2.8)
A = Point(f)
a_1 = Ray(R, A)
B = Intersect(c_a, a_1)
k_1 = AffineRatio(R, B, A)
a_2 = Ray(O, O + Vector[R, A])
C = Intersect(d_a, a_2)
C' = Dilate(C, k_1, O)
C'' = If(k_1 < 1, C')
loc1 = Locus(C'', A)
D = Point(yAxis)
a_3 = Ray(R, D)
E = Intersect(c_a, a_3)
a_4 = Ray(O, Vector[R, E])
F = Intersect(d_a, a_4)
k_2 = AffineRatio(R, E, D)
F' = Dilate(F, k_2, O)
F'' = If(k_2 < 1, F')
loc2 = Locus(F'', D)
G = Point(xAxis)
a_5 = Ray(R, G)
H = Intersect(c_a, a_5)
k_3 = AffineRatio(R, H, G)
a_6 = Ray(O, Vector[R, H])
I = Intersect(d_a, a_6)
I' = Dilate(I, k_3, O)
I'' = If(k_3 < 1, I')
loc3 = Locus(I'', G)
a_8 = Ray(O, Vector[R, K])
L = Intersect(d_a, a_8)
k_4 = AffineRatio(R, K, J)
L' = Dilate(L, k_4, O)
L'' = If(k_4 < 1, L')
loc4 = Locus(L'', J)
List_2 = Sequence(Segment[(k, -8), (k, 7)], k, -3, 16)
M = Point(List_2)
a_9 = Ray(R, M)
N = Intersect(c_a, a_9)
k_5 = AffineRatio(R, N, M)
a_{10} = Ray(O, Vector[R, M])
P = Intersect(d_a, a_{10})
P' = Dilate(P, k_5, O)
P'' = If(k_5 < 1, P')
loc5 = Locus(P'', M)
Q_2: 0.3 * Corner[2] + 0.7 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
poly1, a, q_2, q_3, b = Polygon(Corner[1], Q_2, Q_3, Corner[4])
u_{y} = Vector((0, y(Q_2)), (0, y(Corner[3])))
t_{Ratio}: "$ 縮放倍數：\;" + (LaTeX[3 / r]) + "倍 $"
b_a: floor(x(R) * 1000) / 1000
b_b: floor(x(R) * 1000 + 1) / 1000
c_b = Circle(O, 2.75)
c = 1 (slider from 1 to 2, step 1)
poly3, d, e, g, h = Polygon(Q_2 + (0.05, 0), Corner[2], Corner[3], Q_3 + (0.02, 0))
u_{x} = Vector((x(Q_2), If[c ≟ 1, 0, -2]), (x(Corner[2]), If[c ≟ 1, 0, -2]))
f_a(x) = 3 * lg(x / 8)
S = Point(f_a)
T = Point(f_a)
S_1: (x(S), -2)
T_1: (x(T), -2)
U = Point(f_a)
U_1: (x(U), -2)
i_a = Segment(S, S_1)
i_c = Segment(T, T_1)
i_b = Segment(U, U_1)
text2: "$ " + (LaTeX[x(R)]) + " $"
text3: "$ " + (LaTeX[b_a]) + " $"
text4: "$ " + (LaTeX[b_b]) + " $"
S_2: (0, y(S))
U_2: (0, y(U))
T_2: (0, y(T))
text5: "$ " + (LaTeX[lg(b_a)]) + " $"
text6: "$ " + (LaTeX[lg(b_b)]) + " $"
i = Segment(S, S_2)
j = Segment(U, U_2)
k = Segment(T, T_2)
f_c = Function(f_a, x(S), x(T))
text1_1: "$ log" + (LaTeX[b_a]) + " = " + (LaTeX[lg(b_a)]) + " $
$log" + (LaTeX[x(R)]) + " =x$
$log" + (LaTeX[b_b]) + " =" + (LaTeX[lg(b_b)]) + " $
$ \frac{x" + (LaTeX[If[b_a < 1, "+", "-"]]) + "" + (LaTeX[abs(lg(b_a))]) + " }{" + (LaTeX[lg(b_b)]) + " " + (LaTeX[If[b_a < 1, "+", "-"]]) + "" + (LaTeX[abs(lg(b_a))]) + " }=\frac{" + (LaTeX[x(R)]) + " -" + (LaTeX[b_a]) + " }{" + (LaTeX[b_b]) + " -" + (LaTeX[b_a]) + " } $
$⇒x≈" + (LaTeX[lg(x(R))]) + " $"