Giải và biện luận bất phương trình :
${\log _a}x + {\log _a}\left( {x - 2} \right) > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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Giải và biện luận theo tham số $a$ :
${\log _a}\left( {x - 1} \right) + {\log _a}x > 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)$
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Với giá trị nào của $m$ thì ta có :
$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\log _2}\left( {7{x^2} + 7} \right) \ge {\log _2}\left( {m{x^2} + 4x + m} \right)$$\forall x \in \,R\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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Cho bất phương trình :
$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\log _5}\left( {{x^2} + 1} \right) > {\log _5}\left( {{x^2} + 4x + m} \right) - 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
Tìm các giá trị của $m$ sao cho khoảng $(2,3)$ thuộc tập nghiệm của $(1)$.
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Đăng bài 26-04-12 01:56 PM
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Giải bất phương trình :
$\sqrt {\frac{1}{2} + \sin \,x} \left[ {{{\log }_{\frac{3}{2} + \sin x}}\left( {{{\sin }^2}x + \frac{{6\sqrt 3 + 9}}{4}} \right) - 2} \right] \ge 0\,\,\,\,\,\,\,\,\,(1)$
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Giải bất phương trình :
${\log _{cos\,x}}{\log _{\sin \,x}}\left( {\sin \,x + cos\,2x} \right) > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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Giải bất phương trình :
${\log _{cos\,x}}{\log _{\sin \,x}}tan\,x > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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Giải bất phương trình :
${\log _{tanx}}\sin \,x > 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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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 :
$\begin{array}{l}
1)\,\,\,\,\,\frac{{{{\log }_5}{{\left( {{x^2} - 4x - 11} \right)}^2} - {{\log }_{11}}{{\left( {{x^2} - 4x - 11} \right)}^3}}}{{2 - 5x - 3{x^2}}} \ge 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,\frac{{{{\log }_2}{{\left( {{x^2} - 2x - 7} \right)}^5} - {{\log }_3}{{\left( {{x^2} - 2x - 7} \right)}^8}}}{{3{x^2} - 13x + 4}} \le 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,\,{\log _3}\left( {5{x^2} + 6x + 1} \right) \le 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,\,{\log _{12}}\left( {6{x^2} - 48x + 54} \right) \le 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\
3)\,\,\,\,{\log _{21}}\left( {{x^2} + 2x - 3} \right) \le 1\,\,\,\\
4)\,\,\,\,{\log _2}\left( {{x^2} - 4x - 5} \right) \le 4
\end{array}$
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Giải bất phương trình :
$\frac{1}{{{{\log }_{\frac{1}{3}}}\sqrt {2{x^2} - 2x + 1} }} > \frac{1}{{{{\log }_{\frac{1}{3}}}\left( {x + 1} \right)}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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Giải các bất phương trình :
$\begin{array}{l}
1)\,\,\,\,{\log _x}125x.\log _{25}^2x < 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,{\log _4}{\log _2}x + {\log _2}{\log _4}x > 1\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Đăng bài 26-04-12 11:17 AM
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Giải bất phương trình :
$\,\,\,\,\,\,\,\,\,\,\,\,\,{\log _{\frac{3}{2}}}\left[ {{{\log }_{\frac{1}{3}}}\left( {\frac{{{x^2}}}{2} + {2^{{{\log }_2}x - 1}}} \right) + 3} \right] \le 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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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 :
$\begin{array}{l}
1)\,\,\,\,\,{\log _x}\frac{{2x + \frac{2}{5}}}{{5\left( {1 - x} \right)}} > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\\
2)\,\,\,{\log _x}\frac{{4x + 1}}{{6\left( {x - 1} \right)}} < 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)
\end{array}$
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Giải bất phương trình :
${\log _{2x}}64 + {\log _{{x^2}}}16 \ge 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$
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Giải bất phương trình :
${\log _x}\left( {x - \frac{1}{4}} \right) \ge 2\,\,\,\,\,\,\,\,\,\,\,\,(1) $
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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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