已知2.5^x=1000,0.25^y=1000,求证:1/x-1/y=1/3

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已知2.5^x=1000,0.25^y=1000,求证:1/x-1/y=1/3
已知2.5^x=1000,0.25^y=1000,求证:1/x-1/y=1/3

已知2.5^x=1000,0.25^y=1000,求证:1/x-1/y=1/3
2.5^x=1000,0.25^y=1000
x=log[2.5,1000] = lg1000 / lg2.5 = 3 / lg2.5
y=log[0.25,1000] = lg1000 / lg0.25 = 3 / lg0.25
1/x - 1/y = lg2.5 /3 - lg0.25 /3
= lg10 /3 = 1/3