大师作文网数学计算（2） 对数函数
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数学计算（2） 对数函数
1.
log4 (125) = (3/2)·log2 (5) ,log√3 (5) = 2log3 (50 = log3 (25) ,
∴原式 = (5/2)·log2 (5)·log3 (2/25) ,而log3 (2/25) = log2 (2)/log2 (25) = 1/[2log2 (5)] ,∴原式 = 5/4
2.
(1 - log6 3)^2 = 1 - 2log6 3 + (log6 3)^2 ,(log6 2)·(log6 18) = (log6 2)·(log6 2 + 2log6 3) = (log6 2)^2 + 2(log6 2)(log6 3) ,
∴(1 - log6 3)^2 + (log6 2)·(log6 18) = 1 - 2log6 3 + [(log6 2)+(log6 3)]^2 = 2 - 2(log6 3) = 2log6 2 = log6 4 ,
∴原式 = (log6 4)/(log6 4) = 1
log4 (125) = (3/2)·log2 (5) ,log√3 (5) = 2log3 (50 = log3 (25) ,
∴原式 = (5/2)·log2 (5)·log3 (2/25) ,而log3 (2/25) = log2 (2)/log2 (25) = 1/[2log2 (5)] ,∴原式 = 5/4
2.
(1 - log6 3)^2 = 1 - 2log6 3 + (log6 3)^2 ,(log6 2)·(log6 18) = (log6 2)·(log6 2 + 2log6 3) = (log6 2)^2 + 2(log6 2)(log6 3) ,
∴(1 - log6 3)^2 + (log6 2)·(log6 18) = 1 - 2log6 3 + [(log6 2)+(log6 3)]^2 = 2 - 2(log6 3) = 2log6 2 = log6 4 ,
∴原式 = (log6 4)/(log6 4) = 1