求证:对于正整数a,b,c和实数x,y,z,w,若a^x=b^y=c^z=70^w,且1/x+1/y+1/z=1/w,则abc=70

由a^x=b^y=c^z=70^w得 xlog70(a)=ylog70(b)=zlog70(z)=w 则w/x=log70(a) w/y=log70(b) w/z=log70(z) 而1/x+1/y+1/z=1/w得w/a+w/b+w/c=1 即log70(a)+log70(b)+log70(z)=1 log70(abc)=1 故abc=70