Tìm $m$ để mỗi bất phương trình sau đây có nghiệm:
$\begin{array}{l}
1)\,\,\,{4^x} - {5.2^x} + m \le 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3)\,\,\,{9^x} + m{.3^x} - 1 < 0\\
2)\,\,{4^x} + {5.2^x} + m > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4)\,\,{9^x} + m{.3^x} + 1 \le 0
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,\,{\left( {{2^x} + {{3.2}^{ - x}}} \right)^{2{{\log }_2}x - {{\log }_2}\left( {x + 6} \right)}} > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,\,\,{\left( {{{4.3}^x} + {3^{ - x}}} \right)^{3{{\log }_3}\left( {x - 1} \right) - {{\log }_3}\left( {x - 1} \right)\left( {2x + 1} \right)}} > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\log _2^2\left( {2 + x - {x^2}} \right) + 3{\log _{\frac{1}{2}}}\left( {2 + x - {x^2}} \right) + 2 \le 0\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{\log _{x + 1}}{\left( {{x^2} + x - 6} \right)^2} \ge 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\\
3)\,\,\,{\log _{9{x^2}}}\left( {6 + 2x - {x^2}} \right) \le \frac{1}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)\\
4)\,\,\,{9^{\sqrt {{x^2} - 3} }} + 3 <28. {3^{\sqrt {{x^2} - 3} - 1}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(4)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,{\log _{\frac{1}{{\sqrt 5 }}}}\left( {{6^{x + 1}} - {{36}^x}} \right) \ge - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,{\log _{\frac{1}{{\sqrt 6 }}}}\left( {{5^{x + 1}} - {{25}^x}} \right) \ge - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1){\left( {{x^2} + x + 1} \right)^x} < 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2){\left( {x - 1} \right)^{{x^2} - 6x + 8}} > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,{\left( {\sqrt 2 + 1} \right)^{\frac{{6x - 6}}{{x + 1}}}} \le {\left( {\sqrt 2 - 1} \right)^{ - x}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{\left( {\sqrt 5 + 2} \right)^{x - 1}} \ge {\left( {\sqrt 5 - 2} \right)^{\frac{{x - 1}}{{x + 1}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\,
\end{array}$
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