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Với $a > 1$ ta có
\({x^{{{\log }_a}\left( {{\rm{ax}}} \right)}}
\ge {\left( {{\rm{ax}}} \right)^4} \Leftrightarrow {\log _a}{{x^{{{\log
}_a}\left( {{\rm{ax}}} \right)}} \ge {{\log }_a}{{\left( {{\rm{ax}}}
\right)}^4}}\)
\(\Leftrightarrow {\log
_a}\left( {{\rm{ax}}} \right).{\log _a}x \ge 4{\log _a}\left(
{{\rm{ax}}} \right)\)
\(\Leftrightarrow {\log _a}\left( {{\rm{ax}}} \right)\left( {{{\log }_a}x - 4} \right) \ge 0\)
Đáp số:\(\left[ \begin{array}{l}
x \ge {a^4}\\
0 < x \le \frac{1}{a}
\end{array} \right.\)
Với $0 < a < 1$ ta có:
\({x^{{{\log
}_a}\left( {{\rm{ax}}} \right)}} \ge {\left( {{\rm{ax}}} \right)^4}
\Leftrightarrow \left( {1 + {{\log }_a}x} \right)\left( {{{\log }_a} -
4} \right) \le 0\)
\(\Leftrightarrow - 1 \le {\log _a}x \le 4 \Leftrightarrow {a^4} \le x \le \frac{1}{a}\)
Đáp số: ${a^4} \le x \le \frac{1}{a}$
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