Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,{\log _2}\left( {\sqrt {{x^2} - 4x} + 3} \right) > {\log _{\frac{1}{2}}}\frac{2}{{\sqrt
{{x^2} - 4x} + \sqrt {x + 1} + 1}} + 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,{\log _{\frac{1}{3}}}\left( {\sqrt {9x - {x^2}} + 3} \right) > {\log _3}\frac{{27}}{{\sqrt
{9x - {x^2}} + \sqrt {5 - {x^2}} }} - 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,{\log _{\frac{1}{7}}}\left( {x + 2} \right)\left( {4 - x} \right) + \frac{1}{2}{\log _{\sqrt
7 }}\left( {4 - x} \right) > - 2{\log _{49}}8\\
2)\,\,\,\,\log \,_9^2x > {\log _3}x.{\log _3}\left( {\sqrt {2x + 1} - 1} \right)\\
3)\,\,\,\,{x^{{{\log }_2}\left( {x + 14} \right)}} + {\log _2}\left( {x + 2} \right) \le {x^6}
\end{array}$
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Giải các bất phương trình:
$\begin{array}{l}
1)\,\,\,\,\,{\log _3}\left( {x + 2} \right)\left( {x + 4} \right) + {\log _{\frac{1}{3}}}\left( {x + 2}
\right) < \frac{1}{2}{\log _{\sqrt 3 }}7\\
2)\,\,\,\,\,{\log _{\frac{1}{2}}}\left( {x + 1} \right)\left( {x + 3} \right) + {\log _2}\left( {x + 3}
\right) > - 2{\log _4}11\\
3)\,\,\,\,\,2{\log _{25}}\left( {1 + x} \right)\left( {3 - x} \right) - \frac{1}{2}{\log _{\sqrt 5 }}\left(
{1 + x} \right) > {\log _{\frac{1}{5}}}\frac{1}{2}
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,{\log _3}\left( {5{x^2} + 6x + 1} \right) \le
0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,{\log _{12}}\left( {6{x^2} - 48x + 54} \right) \le
2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\\
3)\,\,\,\,{\log _{21}}\left( {{x^2} + 2x - 3} \right) \le 1\,\,\,\\
4)\,\,\,\,{\log _2}\left( {{x^2} - 4x - 5} \right) \le 4
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,\frac{{\sqrt {x - 5} }}{{{{\log }_{\sqrt 2 }}\left( {x - 4} \right) - 1}} \ge
0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,\frac{{{{\log }_{\sqrt 2 }}{{\left( {x - 3} \right)}^2}}}{{{x^2} - 4x - 5}} \ge
0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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