代數與最小值 (2)

(a)
(3 ‒ √3)ⁿ>10⁹
log(3 ‒ √3)ⁿ>log10⁹
n*log(3 ‒ √3)>9
n>9/log(3-√3)
n>87.29...
So, the smallest possible value of n is 88

(b)
If n=300, P=(3 ‒ √3)^300
10ⁿ⁻¹ < (3 ‒ √3)^300 < 10ⁿ
log10ⁿ⁻¹ < log(3 ‒ √3)^300 < log10ⁿ
n-1 < 300* log(3 ‒ √3) < n
n-1< 30.93 < n
So, n is 31