Question

已知x,y为正实数,满足1≤lg(xy)≤2,3≤lg≤4,求lg(x⁴y²)的取值范围.

Answer

6≤lg(x4y2)≤10

【解析】设a=lgx,b=lgy,则lg(xy)=a+b,

lg=a-b,lg(x4y2)=4a+2b,

设4a+2b=m(a+b)+n(a-b),

∴解得

∴lg(x4y2)=3lg(xy)+lg,

∵3≤3lg(xy)≤6,3≤lg≤4,∴6≤lg(x4y2)≤10.