gbu94mz95e的部落格

標題:

數學問題！！！！！１０分

發問:

log2=0.3101及log3=0.4771 在不使用計算機的情況下，求log18的10次方(須展示計算步驟) 透過証明10的12次方<18的10次方<10的13次方,證明18的10次方是13位數字 在不使用計算機的情況下,求log(3成10的12次方)及log(4成10的12次方)由此，找出18的10次方的最左方數字

最佳解答:

• 講一首慘歌歌詞有 42 點,,,@1@
• psp改左5.50 load 唔到 game
• 考考你iq題@1@

• 講一首慘歌歌詞有 42 點,,,@1@
• psp改左5.50 load 唔到 game
• 考考你iq題@1@

 

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log18 = log(2x(3^2)) = log 2 + log (3^2) = log 2 + 2 log 3 = 0.3010 + 2 x 0.4771 = 1.2552 log(18^10) = 10 log 18 = 10 (1.2552) = 12.552 [Remark: log 2 should be = 0.3010] Since log(10^12) = 12 and log(10^13) = 13, log(10^12) < log(18^10) = 12.552 < log(10^13) and hence 10^12 < 18^10 < 10^13. Since 10^12 has 13 digits (first digit is 1 and then 12 0's) and 10^13 has 14 digits (first digit is 1 followed by 13 0's), the number of digits 18^10 must have 13 digits. log(3x10^12) = log3 + log10^12 = 0.4771 + 12 = 12.4771 log(4x10^12) = log 4 + log10^12 = log (2^2) + 12 = 2 log 2 + 12 = 12.6020 Since log(3x10^12) < log(18^10) < log(4x10^12), 3x10^12 < 18^10 < 4 x10^12 and hence the most significant digit (leftmost digit) is 3.

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