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

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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