$ 首數與位數的關係 $

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$ 顯示\;n $

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a = 2 (slider from 2 to 9, step 1)
n = 15 (slider from 2 to 30, step 1)
list2: {0, 0.301, 0.4771, 0.602, 0.699, 0.7781, 0.8451, 0.903, 0.9542, 1}
u: (n * Element[list2, a])
v: u - floor(u)
list3 = Sequence(v - 1 + Element[list2, k], k, 1, 10)
list4 = KeepIf(x ≥ 0, list3)
list1: {"0", "0.3010", "0.4771", "0.6020", "0.6990", "0.7781", " 0.8451", " 0.9030", " 0.9542", "1"}
b = Element(list1, 10 - Length[list4])
c = Element(list1, 11 - Length[list4])
c_1 = IndexOf(c, list1)
b_1 = IndexOf(b, list1)
text10: "$list1=" + (LaTeX[list1]) + "$
$list2=" + (LaTeX[list2]) + "$
$list3= " + (LaTeX[list3]) + " $
$list4=" + (LaTeX[list4]) + "$"
d = false
Step = 0 (slider from 0 to 11, step 1)
t1: "$ log\;n=log\;" + (LaTeX[a]) + "^{-" + (LaTeX[n]) + "} $"
t2: "$ =-" + (LaTeX[n]) + "\cdot log\;" + (LaTeX[a]) + " $"
t3: "$ =-" + (LaTeX[n]) + "×" + (LaTeX[Element[list1, a]]) + " $"
t9: "$ 小數點後第\;" + (LaTeX[floor(u) + 1]) + " \;位起始出現不為\;0\;的數字$"
w: 1 - v
tb: "$ 故第一個出現不為\;0\;的數字為\;" + (LaTeX[b_1]) + " $"
text2: "$\;\;\;\;\;n=" + (LaTeX[a]) + "^{-" + (LaTeX[n]) + "}=\frac{1}{" + (LaTeX[a^(n)]) + "}  =" + (LaTeX[ScientificText[a^((-n)), 4]]) + "$"
A = Corner(4)
t4: "$ =-" + (LaTeX[If[Mod[(10000 * u), 1000] ≟ 0, u + ".000", If[Mod[(10000 * u), 100] ≟ 0, u + "00", If[Mod[(10000 * u), 10] ≟ 0, u + "0", If[Mod[(10000 * u), 10] ≠ 0, u + ""]]]]]) + " $"
t5: "$ =-" + (LaTeX[floor(u)]) + " -" + (LaTeX[If[Mod[(10000 * v), 1000] ≟ 0, v + ".000", If[Mod[(10000 * v), 100] ≟ 0, v + "00", If[Mod[(10000 * v), 10] ≟ 0, v + "0", If[Mod[(10000 * v), 10] ≠ 0, v + ""]]]]]) + "$"
t6: "$ =(-" + (LaTeX[floor(u)]) + "\fgcolor{255,153,204}{-1})\fgcolor{255,153,204}{+}(\fgcolor{255,153,204}{1}-" + (LaTeX[If[Mod[(10000 * v), 1000] ≟ 0, v + ".000", If[Mod[(10000 * v), 100] ≟ 0, v + "00", If[Mod[(10000 * v), 10] ≟ 0, v + "0", If[Mod[(10000 * v), 10] ≠ 0, v + ""]]]]]) + ") $"
t7: "$ =-" + (LaTeX[floor(u) + 1]) + " +" + (LaTeX[If[Mod[(10000 * (1 - v)), 1000] ≟ 0, 1 - v + ".000", If[Mod[(10000 * (1 - v)), 100] ≟ 0, 1 - v + "00", If[Mod[(10000 * (1 - v)), 10] ≟ 0, 1 - v + "0", If[Mod[(10000 * (1 - v)), 10] ≠ 0, 1 - v + ""]]]]]) + "$"
t8: "$ n\;的首數為\;" + (LaTeX[(-floor(u)) - 1]) + " ，\;尾數為\;" + (LaTeX[If[Mod[(10000 * w), 1000] ≟ 0, w + ".000", If[Mod[(10000 * w), 100] ≟ 0, w + "00", If[Mod[(10000 * w), 10] ≟ 0, w + "0", If[Mod[(10000 * w), 10] ≠ 0, w + ""]]]]]) + "\;$"
ta: "$ 又log\;" + (LaTeX[b_1]) + "=" + (LaTeX[b]) + "≤" + (LaTeX[If[Mod[(10000 * w), 1000] ≟ 0, w + ".000", If[Mod[(10000 * w), 100] ≟ 0, w + "00", If[Mod[(10000 * w), 10] ≟ 0, w + "0", If[Mod[(10000 * w), 10] ≠ 0, w + ""]]]]]) + "<" + (LaTeX[c]) + " =log\;" + (LaTeX[c_1]) + "$"
Question_1: "$若\;n= " + (LaTeX[a]) + "^{-" + (LaTeX[n]) + "}，\;試求小數點後第幾位起始出現不為0的數？又此數$
$字為何？(\;已知：\;log2=0.3010,\;log3=0.4771,\;log7=0.8451\;)$"