Question

每天努力一點點

求講解 謝謝

7. 已知正整數n滿足2”為10位數且最高數字為4,求n=
(log 2 0.3010, log 3 ≈ 0.4771)
06020
Ans:
AX03010
=
19+06~
1100
≤x≤2

Answer 1

✨ Jawaban Terbaik ✨

qn

log(2ⁿ) = log(4.⋯×10⁹)
n log2 ≈ log4 + 9 ≈ 9.6020
n ≈ 9.6020/0.3010 ≈ 31.90
n ≈ 32

qn

嚴謹一點來寫的話
4×10⁹ ≤ 2ⁿ < 5×10⁹
log4 + 9 ≤ n log2 < log5 + 9
(9+2log2)/log2 ≤ n < (9+log5)/log2
31.9 ≤ n < 32.2
n = 31