Question

已知25的x次方为2000,80的y次方为2000.求证xy=x+y.

Answer 1

25^x=2000,80^y=2000,

x=lg2000/lg25,y=lg2000/lg80

x+y=lg2000/lg25=(3+lg2)/(2lg5)=(3+lg2)/(2(1-lg2)),

y=lg2000/lg80=(3+lg2)/(1+3lg2),

x+y=(3+lg2)/(2(1-lg2))+(3+lg2)/(1+3lg2)

=(3+lg2)^2/((2(1-lg2))(1+3lg2))=xy

另解看图片