Question

若a^x=b^y=(ab)^xy,证明x+y=1

Answer 1

a^x = b^y = (ab)^xy => a^x = a^xy*b^xy =>

a^x = (a^x)^y* (b^y)x = (a^x)^y*(a^x)^x) = (a^x)^(x+y)

=> (a^x)^1 = (a^x)^(x+y) => x+y =1