x,y,z是正实数,且1/2 lgx+1/3 lgy+1/4 lgz=1,则x的6次方乘以y的4次方乘以z的3次方=?
问题描述：
x,y,z是正实数,且1/2 lgx+1/3 lgy+1/4 lgz=1,则x的6次方乘以y的4次方乘以z的3次方=?
答
1/2 lgx+1/3 lgy+¼ lgz=lg{[x^(1/2)][y^(1/3)][z^(1/4)]}=1
[x^(1/2)][y^(1/3)][z^(1/4)]=10
{[x^(1/2)][y^(1/3)][z^(1/4)]}^12=10^12
(x^6)(y^4)(z^3)=10^12
所以是10的12次方