已知3.65的x次方=1000,0.00365的y次方=1000,求1/x-1/y的值∵3.65的x次方=1000，0.00365的y次方=1000∴3.65^xy==1000^y,0.00365^xy=1000^x两式相除得1000^xy=1000^(y-x)∴xy=y-x∴x分之1-y分之1=(y-x)/xy=1

Question

已知3.65的x次方=1000,0.00365的y次方=1000,求1/x-1/y的值
∵3.65的x次方=1000，0.00365的y次方=1000
∴3.65^xy==1000^y,0.00365^xy=1000^x
两式相除得1000^xy=1000^(y-x)
∴xy=y-x
∴x分之1-y分之1=(y-x)/xy=1

Answer 1

3.65^x=1000,0.00365^y=1000,0.00365=3.65/1000=3.65/3.65^x=3.65^(1-x)0.00365^y=10003.65^[(1-x)]^y=1000=3.65^x从而：(1-x)*y=x,y-xy=x 即：y-x=xy,两边同时除以xy,1/x-1/y=1