$ 首數與位數的關係 $

1

$ 顯示\;n $

a = 2 (slider from 2 to 10, step 1)
n = 2 (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 - Element[list2, k], k, 1, 10)
list4 = KeepIf(x ≥ 0, list3)
t1: "$ log\;n=log\;" + (LaTeX[a]) + "^{" + (LaTeX[n]) + "} $"
t2: "$ =" + (LaTeX[n]) + "\cdot log\;" + (LaTeX[a]) + " $"
list1: {"0", "0.3010", "0.4771", "0.6020", "0.6990", "0.7781", " 0.8451", " 0.9030", " 0.9542", "1"}
t4: "$ =" + (LaTeX[u]) + " $"
t5: "$ n\;的首數為\;" + (LaTeX[floor(u)]) + " ，\;尾數為\;" + (LaTeX[v]) + "\;$"
t6: "$ n\;為\;" + (LaTeX[floor(u) + 1]) + " \;位數$"
b = Element(list1, IndexOf[Min[list4], list4])
t3: "$ =" + (LaTeX[n]) + "×" + (LaTeX[Element[list1, a]]) + " $"
c = Element(list1, Length[list4] + 1)
c_1 = IndexOf(c, list1)
b_1 = IndexOf(b, list1)
text10: "$list1=" + (LaTeX[list1]) + "$
$list2=" + (LaTeX[list2]) + "$
$list3= " + (LaTeX[list3]) + " $
$list4=" + (LaTeX[list4]) + "$"
t7: "$ 又log\;" + (LaTeX[b_1]) + "=" + (LaTeX[b]) + "≤" + (LaTeX[v]) + "<" + (LaTeX[c]) + " =log\;" + (LaTeX[c_1]) + "$"
d = false
Step = 0 (slider from 0 to 8, step 1)
t8: "$ 故\;n\;的最高位數字為\;" + (LaTeX[b_1]) + " $"
text1: "$若\;n= " + (LaTeX[a]) + "^{" + (LaTeX[n]) + "}，\;試求n為幾位數？又n的最高位數字為何？$
$(\;已知：\;log2=0.3010,\;log3=0.4771,\;log7=0.8451 \;)$"
text2: "$  n=" + (LaTeX[a]) + "^{" + (LaTeX[n]) + "}=" + (LaTeX[a^(n)]) + "$"