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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 :
$\begin{array}{l}
1)\,\,\,{\log _3}\left( {{x^2} - 2} \right) < {\log _3}\left( {\frac{3}{2}\left| x \right| - 1} \right)\\
2)\,\,{\log _{\frac{1}{2}}}{\left( {4 - x} \right)^2} > {\log _{\frac{1}{2}}}\left( {6\left| x \right| - 3} \right)\\
3)\,\,\,{\log _4}\left( {{x^2} - 5} \right) < {\log _4}\left( {\frac{7}{3}\left| x \right| - 3} \right)\\
4)\,\,\,{\log _{\frac{1}{3}}}\left( {3 - {x^2}} \right) > {\log _{\frac{1}{3}}}\left( {4\left| x \right| - 2} \right)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,{\log _4}\sqrt[3]{x} - {\log _2}x > 2\\
2)\,\,\,\,{\log _3}\sqrt x - 2{\log _9}x > 2\\
3)\,\,\,\,15{\log _5}\sqrt[5]{x} - 2{\log _{\sqrt 5 }}x > 6\\
4)\,\,\,\,2{\log _7}\sqrt x - {\log _{\sqrt 7 }}x > 4\\
5)\,\,\,\,3{\log _2}\sqrt[3]{x} - 4{\log _4}x > 2
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\log _2^2\left( {2 - x} \right) - 8{\log _{\frac{1}{4}}}\left( {2 - x} \right) \ge 5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\log _5^2\left( {6 - x} \right) + 2{\log _{\frac{1}{5}}}\left( {6 - x} \right) - {\log _3}27 \ge 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,{\log _{{x^2}}}\left( {3 - 2x} \right) > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,{\log _x}\frac{3}{{8 - 2x}} > - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\\
3)\,\,{\log _{{x^2}}}\frac{{2x}}{{\left| {x - 3} \right|}} \le \frac{1}{{2\,}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,{\log _{\frac{1}{3}}}\sqrt {x + 6} \le {\log _{\frac{1}{3}}}\left( {x + 4} \right)\\
2)\,\,\,\,\frac{1}{2}{\log _{\frac{1}{5}}}\left( {x + 8} \right) \ge {\log _{\frac{1}{5}}}\left( {x - 4} \right)\\
3)\,\,\,\,{\log _{\frac{1}{2}}}\sqrt {5 - x} < {\log _{\frac{1}{2}}}\left( {3 - x} \right)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,{\log _{\frac{1}{2}}}\left( {x - \frac{1}{2}} \right) + \,\,{\log _{\frac{1}{2}}}\left( {x - 1} \right) \le 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,{\log _{\frac{1}{2}}}\left( {x + \frac{1}{2}} \right) + \,\,{\log _{\frac{1}{2}}}x \ge 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1){\log _{\frac{1}{2}}}\left( {1 + x - \sqrt {{x^2} - 4} } \right) \le 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3)\,\,{\log _{\frac{1}{5}}}\left( { - x + 1} \right) \le 0\\
2)\,{\log _3}\left( {\sqrt {{x^2} - 9} - x + \frac{1}{3}} \right) \le - 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4)\,{\log _2}\left( {2 - x - \sqrt {{x^2} - 1} } \right) \ge 1
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,{\log _2}\frac{x}{{x - 1}} \le 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2)\,\,{\log _{\frac{1}{2}}}\frac{{3x + 1}}{{x + 1}} \ge - 1\\
3)\,\,{\log _{\frac{1}{4}}}\frac{{x - 3}}{{x + 3}} \le - \frac{1}{2}
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,{\log _2}x < 5\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,3{\log _8}\left( {x - 2} \right) - 6{\log _8}\left( {x - 1} \right) > - 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\\
3)\,{\log _2}\left( {{x^2} - 1} \right) \ge 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)\\
4)\,{\log _2}\left( {x + 1} \right) - {\log _{x + 1}}64 < 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(4)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1){\log _5}\left( {26 - {3^x}} \right) > 2 \,\,\,\,\,(1)\\
2){\log _3}\left( {13 - {4^x}} \right) > 2 \,\,\,\,\,(2)
\end{array}$
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