Question

已知25^x=2000,80^y=2000,求xy-x-y的值

Answer 1

因为25^x=2000 ,80^y=2000

所以 (25^x)^y=2000^y ,(80^y)^x=(2000)^x

即

25^xy = 2000^y (1)

80^xy = 2000^x (2)

(1)*(2)得

25^xy * 80^xy = 2000^y * 2000^x

即 2000^xy = 2000^(y+x)

即xy = x+y

所以xy-x-y = xy-(x+y)=0