如题所述
易见,x,y,z同号。
当x,y,z都为正时:
2^x=3^y>(2根号2)^y=2^(1.5y) ==> x>1.5y ==> 2x>3y
2^x=5^z<(4根号2)^z =2^(2.5z) ==> x<2.5z ==>2x<5z
从而3y<2x<5z
当x,y,z都为负时:
2^x=3^y<(2根号2)^y=2^(1.5y)==> x<1.5y ==> 2x<3y
2^x=5^z>(4根号2)^z =2^(2.5z) ==> x>2.5z ==>2x>5z
从而5z<2x<3y
综合得:当x,y,z都大于0时,3y<2x<5z;当x,y,z都小于0时,5z<2x<3y.
当x,y,z都为正时:
2^x=3^y>(2根号2)^y=2^(1.5y) ==> x>1.5y ==> 2x>3y
2^x=5^z<(4根号2)^z =2^(2.5z) ==> x<2.5z ==>2x<5z
从而3y<2x<5z
当x,y,z都为负时:
2^x=3^y<(2根号2)^y=2^(1.5y)==> x<1.5y ==> 2x<3y
2^x=5^z>(4根号2)^z =2^(2.5z) ==> x>2.5z ==>2x>5z
从而5z<2x<3y
综合得:当x,y,z都大于0时,3y<2x<5z;当x,y,z都小于0时,5z<2x<3y.
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