log(2)x=log(3)y=log(5)z>0,比较x^(1/2)、y^(1/3)、z^(1/5) 设log2,x=log3,y=log5,z=t>0 ==>x=2^t,y=3^t,z=5^t ==>x^(1/2)=2^(t/2),y^(1/3)=3^(t/3),z^(1/5)=5^(t/5) 设m=x^(1/2)=2^(t/2),n=y^(1/3)=3^(t/3),p=z^(1/5)=5^(t/5) ==>m^6-n^6=[2^(t/2)]^6-[3^(t/3)]^6=2^(3t)-3^(2t)=8^t-9^tm^6m ==>m^10>p^10 ==>m>p 所以,p