正实数a，b，c，x，y，z，w，满足a^x=b^y=c^=154^w,且1/x+1/y+1/z=1/w，则abc=？-百谷歌

由a^x=b^y=c^z=154^w得 xlog154(a)=ylog154(b)=zlog154(z)=w 则w/x=log154(a) w/y=log154(b) w/z=log154(z) 而1/x+1/y+1/z=1/w得w/a+w/b+w/c=1 即log154(a)+log154(b)+log154(z)=1 log154(abc)=1 故abc=154