標題:
此文章來自奇摩知識+如有不便請留言告知
F4 maths 對數
發問:
若s=log2 及t=log3,試以s和t表示下列各項。 1. log√ 72 若 p=log3及q=log5,試以p和q表示下列各項。 1. log 0.36 2. log√ 24
最佳解答:
若s = log 2 及t = log 3, 試以 s 和 t 表示下列各項。 1. log √ 72 log √72 = (1/2) log 72 = (1/2) log (8 x 9) = (1/2) log (2^3 x 3^2) = (1/2) (3 log 2 + 2 log 3) = (1/2) (3s + 2t) 若 p = log 3及q = log 5, 試以 p 和 q 表示下列各項。 1. log 0.36 2. log√ 24 log 0.36 = log (36 / 100) = log (9 / 25) = log9 - log25 = log3^2 - log5^2 = 2log3 - 2log5 = 2p - 2q log √24 = (1/2) log 24 = (1/2) log (3 x 8) = (1/2) log (3 x 1000 / 125) = (1/2) [log 3 - log 125 + log 1000] = (1/2) [log 3 - log 5^3 + log 10^3] = (1/2) [log 3 - 3 log 5 + 3 log 10] = (1/2) (p - 3q + 3)
其他解答:
其實尾二那步還沒有錯的...|||||螞蟻雄兵 ( 知識長 ) In question 2 the answer should be (p-3q+3)/2 !|||||若s=log2 及t=log3，試以s和t表示log√72 log√ 72 =(1/2)log72 =(1/2)log[(2^3)*(3^2)] =(3/2)log2+log3 =(3/2)s+t 若 p=log3及q=log5，試以p和q表示下列各項 1. log 0.36 Sol q=log5=1－log2 log2=1－q log0.36 =log36－log100 =log[(2^2)*(3^2)]－2 =2log2+2log3－2 =2(1－q)+2p－2 =2p－2q 2. log√ 24 Sol log√ 24 =(1/2)log24 =(1/2)log[(2^3)*3] =(3/2)log2+(1/2)log3 =(3/2)*(1－q)+(1/2)p =p/2－q/2+3/2
留言列表
