对于正整数a,b,c(a≤b≤c)和实数x,y,z,w,若a^x=b^y=c^z=70^w≠1,1/x+1/y+1/z=1/w,求a,b,c的值.

a^x=b^y=c^z=70^w=k≠1,
x=logak,y=logbk,z=logck,w=log70k
1/x=logka,1/y=logkb,1/z=logkc,1/w=logk(70)
1/x+1/y+1/z=logka+logkb+logkc=logk(abc)
1/x+1/y+1/z=1/w
所以,logk(abc)=logk(70)
abc=70