高一数学题，怎么做？
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x^(log<a>x) < a^3.x^2
=> x >0 (1)
x^(log<a>x) < a^3.x^2
x^(log<a>x) < x^(2+ log<x>a^3)
log<a>x < 2+ log<x>a^3
log<a>x < 2+ 3/log<a> x
[ (log<a>x)^2 - 2log<a>x - 3 ]/ log<a> x < 0
(log<a>x -3)(log<a>x +1)/log<a> x < 0
log<a>x < -1 or 0< log<a>x < 3
0<x<1/a or 1<x<a^3 (2)
(1) and (2)
=>
0<x<1/a or 1<x<a^3
=> x >0 (1)
x^(log<a>x) < a^3.x^2
x^(log<a>x) < x^(2+ log<x>a^3)
log<a>x < 2+ log<x>a^3
log<a>x < 2+ 3/log<a> x
[ (log<a>x)^2 - 2log<a>x - 3 ]/ log<a> x < 0
(log<a>x -3)(log<a>x +1)/log<a> x < 0
log<a>x < -1 or 0< log<a>x < 3
0<x<1/a or 1<x<a^3 (2)
(1) and (2)
=>
0<x<1/a or 1<x<a^3
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