Trắc nghiệm Bất phương trình mũ và bất phương trình lôgarit Toán Lớp 12

A. \(\left( { – \infty ;\,1} \right] \cup \left[ {2;\, + \infty } \right)\)

B. \(\left( { – \infty ;\, – \frac{3}{2}} \right) \cup \left( { – \frac{1}{2};\,1} \right] \cup \left[ {2;\, + \infty } \right)\)

C. \(\left( { – \infty ;\, – \frac{3}{2}} \right] \cup \left[ { – \frac{1}{2};\,1} \right] \cup \left[ {2;\, + \infty } \right)\)

D. \(\;\left( { – \infty ;\, – \frac{3}{2}} \right) \cup \left( { – \frac{1}{2};\,1} \right) \cup \left( {2;\, + \infty } \right)\)

A. \({S_1} \subset {S_2} \subset {S_3}\)

B. \({S_1} \subset {S_3} \subset {S_2}\)

C. \({S_3} \subset {S_1} \subset {S_2}\)

D. \({S_3} \subset {S_2} \subset {S_1}\)

A. \(\left[ {0; + \infty } \right)\)

B. \(\left[ {0;2} \right]\)

C. \(\left[ {2; + \infty } \right)\)

D. \(\left[ {2; + \infty } \right) \cup \left\{ 0 \right\}\)

A. Bất phương trình đã cho có tập nghiệm \(T = \left( { – \infty ;1 – \sqrt {{{\log }_{\frac{5}{2}}}5} } \right) \cup \left( {1 + \sqrt {{{\log }_{\frac{5}{2}}}5} ; + \infty } \right) \cup \left( {0;2} \right)\).

B. Bất phương trình đã cho vô nghiệm.

C. Tập xác định của phương trình đã cho là \(\left( {0; + \infty } \right)\).

D. Bất phương trình đã cho có vô số nghiệm.

A. \(S = \left( { – 1;0} \right] \cup \left( {1; + \infty } \right).\)

B. \(S = \left( { – 1;0} \right] \cap \left( {1; + \infty } \right).\)

C. \(S = \left( { – \infty ;0} \right].\)

D. \(S = \left( { – \infty ;0} \right).\)

A. \(0 \le x < 1\)

B. \(0 < x \le 1\)

C. 0 < x < 1

D. \(0 \le x \le 1\)

A. \(\left[ {\begin{array}{*{20}{c}}{x < – \frac{1}{2}}\\{x > 1}\end{array}} \right.\)

B. \(– \frac{1}{2} < x < 1\)

C. x > 1

D. \(x < – \frac{1}{2}\)

A. 1

B. 0

C. 9

D. 11

A. \(\left[ {0;{\rm{ }}2} \right]\)

B. \(\left( { – \infty ;{\rm{ }}1} \right]\)

C. \(\left( { – \infty ;{\rm{ }}0} \right]\)

D. \(\left[ {2; + \infty } \right)\)

A. \(\left( { – \infty ;1} \right) \cup \left( {2; + \infty } \right)\)

B. \(\left( { – \infty ;1} \right) \cup \left( {2;5} \right)\)

C. \(\left( { – \infty ;1} \right) \cup \left( {5; + \infty } \right)\)

D. \(\left( {1;2} \right) \cup \left( {5; + \infty } \right)\)

A. \(\left( { – \infty ; – 1} \right) \cup \left( {2;3} \right)\)

B. \(\left( { – \infty ;1} \right) \cup \left( {2;3} \right)\)

C. \(\left( {2;3} \right)\)

D. \(\left( { – \infty ; – 2} \right) \cup \left( {2;3} \right)\)

A. \(2 \le x\)

B. \(1 \le x \le 2\)

C. \(2 \le x \le 7\)

D. \(2 \le x \le 4\)

A. \(S = \left[ {1; + \infty } \right) \cup \left\{ 0 \right\}\)

B. \(S = \left[ {1; + \infty } \right)\)

C. \(S = \left[ {0; + \infty } \right)\)

D. \(S = \left[ {2; + \infty } \right) \cup \left\{ 0 \right\}\)

A. \(– 1 < x \le 1\)

B. \(x \le – 1\)

C. x > 1

D. 1 < x < 2

A. \(\left[ { – 1;1} \right]\)

B. \(\left( { – \infty ; – 1} \right) \cup \left( {1; + \infty } \right)\)

C. \(\left[ {{{\log }_6}\frac{2}{3};{{\log }_6}\frac{3}{2}} \right]\)

D. \(\left( { – \infty ;{{\log }_6}2} \right)\)

A. \(\left( {0;1} \right)\)

B. \(\left( {1;2} \right)\)

C. \(\left\{ {\frac{1}{3}} \right\}\)

D. \(\left( {2;3} \right)\)

A. \(\left( { – \infty ;1} \right)\)

B. \(\left( { – \infty ; – 2} \right) \cup \left( {3; + \infty } \right)\)

C. \(\left( {1; + \infty } \right)\)

D. \(\left( { – 2;3} \right)\)

A. x < \frac{1}{2}\) hoặc x > 2

B. \(\frac{1}{2} < x < 2\)

C. \(– \ln 2 < x < \ln 2\)

D. x < – \ln 2\) hoặc \(x > \ln 2

A. 1

B. 2

C. 3

D. 4

A. \(S = \left( { – \infty ; + \infty } \right)\)

B. \(S = \left( { – \infty ;3} \right]\)

C. \(S = \left( {3; + \infty } \right)\)

D. \(S = \left( { – \infty ;3} \right)\)

A. \(T = \left( { – \infty ;\,{{\log }_{\frac{4}{5}}}\frac{{31}}{{13}}} \right].\)

B. \(T = \left[ {{{\log }_{\frac{4}{5}}}\frac{{31}}{{13}};\, + \infty } \right).\)

C. \(T = \left( { – \infty ;\,{{\log }_{\frac{4}{5}}}\frac{{31}}{{13}}} \right).\)

D. \(T = \left( {{{\log }_{\frac{4}{5}}}\frac{{31}}{{13}};\, + \infty } \right).\)

A. \(x \in \left( {0;{{\log }_{\frac{3}{2}}}3} \right].\)

B. \(x \in \left( {1;3} \right).\)

C. \(x \in \left( {1;3} \right].\)

D. \(x \in \left[ {0;{{\log }_{\frac{3}{2}}}3} \right].\)

A. \(\left[ \begin{array}{l}x < 0\\x > 2\end{array} \right.\)

B. x < 0

C. x > 2

D. 0 < x < 2

A. \(\left[ \begin{array}{l}x > 1\\x < {\log _3}2\end{array} \right.\)

B. \(x > {\log _3}2\)

C. x < 1

D. \({\log _3}2 < x < 1\)

A. \(x \in \left[ {2; + \infty } \right)\)

B. \(x \in \left( {2; + \infty } \right)\)

C. \(x \in \left( { – \infty ;2} \right)\)

D. \(\left( {2; + \infty } \right)\)

A. 2

B. 4

C. 6

D. 3

A. \(x \le \frac{2}{3}\)

B. \(x > \frac{2}{3}\)

C. \(x \ne \frac{2}{3}\)

D. \(x = \frac{2}{3}\)

A. \(\left( { – \infty ; – 1} \right] \cup \left[ {0;1} \right]\)

B. \(\left[ { – 1;0} \right]\)

C. \(\left( { – \infty ; – 1} \right) \cup \left[ {0; + \infty } \right)\)

D. \(\left[ { – 1;0} \right] \cup \left( {1; + \infty } \right)\)

A. \(\left( { – \infty ;\frac{2}{3}} \right]\)

B. \(\left[ { – \frac{2}{3}; + \infty } \right)\)

C. \(\left( { – \infty ;\frac{2}{5}} \right]\)

D. \(\left[ {\frac{2}{5}; + \infty } \right)\)

A. \(S = \left( { – \infty ;\frac{{ – 2}}{5}} \right)\)

B. \(S = \left( { – \infty ;\frac{{ – 2}}{5}} \right) \cup \left( {0; + \infty } \right).\)

C. \(S = \left( {0; + \infty } \right).\)

D. \(S = \left( {\frac{{ – 2}}{5}; + \infty } \right).\)

A. \(\left( { – \infty ;\,\, – 2} \right)\)

B. \(\left( { – \infty ;\,\, – 2} \right) \cup \left( {1;\,\, + \infty } \right)\)

C. \(\left( { – 2;\,\,1} \right)\)

D. \(\left( {1;\,\, + \infty } \right)\)

A. \(\left[ {_{x < 1}^{x > 2}} \right.\)

B. 2 < x < 4

C. 1 < x < 2

D. 0 < x < 2

A. x > 3 hoặc x < – 3

B. – 3 < x < 3

C. x < – 3

D. x > 3

A. \(x \ge – 4\)

B. x < 0

C. x > 0

D. x < 4

A. \(S = \left( { – \infty ;3} \right)\)

B. \(S = \left( {3; + \infty } \right)\)

C. \(S = \left( { – \infty ; – 3} \right)\)

D. \(S = \left( { – \frac{1}{2};3} \right)\)

A. \(\left( { – \infty ; – \frac{2}{3}} \right)\)

B. \(\left( {0; + \infty } \right)\backslash \left\{ 1 \right\}\)

C. \(\left( { – \infty ;0} \right)\)

D. \(\left( { – \frac{2}{3}; + \infty } \right)\)

A. \(\left( { – \infty ; – \frac{1}{3}} \right)\)

B. \(\left( {1; + \infty } \right)\)

C. \(\left( { – \frac{1}{3};1} \right)\)

D. \(\left( { – \infty ; – \frac{1}{3}} \right) \cup \left( {1; + \infty } \right)\)

A. Sai ở bước 1

B. Sai ở bước 2

C. Sai ở bước 3

D. Đúng.

A. 3

B. 4

C. 5

D. 6

A. \(S = \left( {2;\, + \infty } \right)\)

B. \(S = \left( { – \infty ;\,0} \right)\)

C. \(S = \left( {0;\, + \infty } \right)\)

D. \(S = \left( { – \infty ;\, + \infty } \right)\)

A. \(x > \frac{2}{3}\)

B. \(x < \frac{2}{3}\)

C. \(x > \frac{3}{2}\)

D. \(x < \frac{3}{2}\)

A. \(\left( { – \infty ;{{\log }_2}3} \right]\)

B. \(\left( { – \infty ;{{\log }_{\frac{2}{3}}}3} \right)\)

C. \(\emptyset\)

D. \(\left( {{{\log }_{\frac{2}{3}}}3; + \infty } \right)\)

A. \(\left[ { – 1;1} \right]\)

B. \(\left( { – \infty ;1} \right]\)

C. \(\left[ { – \sqrt 7 ;\sqrt 7 } \right]\)

D. \(\left[ {1; + \infty } \right)\)

A. x=1

B. x=2

C. x=1;x=2

D. x=0

A. 0

B. 1

C. 2

D. Vô số.

A. \(S=\left(0 ; \frac{1}{2}\right) \cup(2 ;+\infty)\)

B. \(S=\left(1 ; \frac{3}{2}\right)\)

C. \(S=(2 ;+\infty)\)

D. \(S=\left[1 ; \frac{3}{2}\right]\)

A. \(\left[\begin{array}{l} x<1 \\ x>3 \end{array}\right.\)

B. \(\left[\begin{array}{l} 0<x<1 \\ x>3 \end{array}\right.\)

C. \(1\le x\le 3\)

D. \(1<x<3\)

A. \(-3\le x\le \frac{1}{25}\)

B. \(\frac{1}{125}\le x\le\frac{1}{25}\)

C. \(-3<x<\frac{1}{5}\)

D. \(\frac{1}{125}<x<\frac{1}{25}\)

A. \(S=\left(1 ;+\infty\right)\)

B. \(S=\left(1 ; \frac{3}{2}\right)\)

C. \(S=[1-\sqrt{2} ; 0] \cup[1+\sqrt{2} ;+\infty) .\)

D. \(S=\left(-\infty ; \frac{3}{2}\right)\)

A. \(S=[1-\sqrt{2} ; 0] \cup[1+\sqrt{2} ;+\infty) \text { . }\)

B. \(S=\left(1 ; \frac{3}{2}\right) .\)

C. \(S=\left(1 ; 2\right) .\)

D. \(S=\left(-\infty; \frac{3}{2}\right) .\)