2^x=3^y=5^z=a
x,y,z均為正數(shù)
所以a>1
lga>0
2^x=3^y=5^z=a
取對數(shù)
xlg2=lga
ylg3=lga
zlg5=lga
所以2x=2lga/lg2=lga/(1/2*lg2)
3y=lga/(1/3*lg3)
5z=lga/(1/5*lg5)
看分母
即2^(1/2),3^(1/3),5^(1/5)
[2^(1/2)]^6=2^3=8
[3^(1/3)]^6=3^2=9
[2^(1/2)]^10=2^5=32
[5^(1/5)]^10=5^2=25
所以
3^(1/3)>2^(1/2)>5^(1/5)
所以1/3*lg3>1/2*lg2>1/5*lg5>0
所以0<1/(1/3*lg3)<1/(1/2*lg2)<1/(1/5*lg5)
lga>0
所以3y<2x<5z