.已知log2, log3, log4, log5, log6, log8, log9，求log7?
回答 (1)
2015-08-19 4:24 am
log4 = 2log2, log5 = log10 - log2 = 1 - log2, log6 = log2 + log3, log8 = 3log2, log9 = 2log3
皆可以log2 及 log3 表示, 故袛需嘗試以 log2 及 log3 去逼近 log7。
log7⁴= log 2401
4log7 ≈ log 2400 = log(4 × 6 × 100) = log4 + log6 + log100 = 2log2 + (log2 + log3) + 2 = 3log2 + log3 + 2
log7 ≈ (3log2 + log3 + 2)/4 ≈ 0.8451。
皆可以log2 及 log3 表示, 故袛需嘗試以 log2 及 log3 去逼近 log7。
log7⁴= log 2401
4log7 ≈ log 2400 = log(4 × 6 × 100) = log4 + log6 + log100 = 2log2 + (log2 + log3) + 2 = 3log2 + log3 + 2
log7 ≈ (3log2 + log3 + 2)/4 ≈ 0.8451。
收錄日期: 2021-04-18 00:05:52
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