Trắc nghiệm Lôgarit Toán Lớp 12

A. A = 3log₃7.

B. A = log₃7.

C. A = 2log₃7

D. A = 4log₃7.

A. 25

B. 625

C. 5

D. 58

A. 2a+ 2ab

B. a+ ab

C. 3a+ ab

D. 2a+ ab

A. \(\frac{3}{{5\left( {1 - a} \right)}}\)

B. \(\frac{5}{{3\left( {1 - a} \right)}}\)

C. \(\frac{1}{{2\left( {1 - a} \right)}}\)

D. \(\frac{1}{{5\left( {1 - a} \right)}}\)

A. \(\frac{{4 + a}}{2}\)

B. \(\frac{{1 + 4a}}{2}\)

C. \(\frac{{4a + 3}}{2}\)

D. \(\frac{{4a-1}}{2}\)

A. 3+ 2a

B. 4+ 2a

C. 4+ a

D. 5- a

A. log_ac + log_bc = log_abc

B. 2log_ab+ 3log_ac = log_a( b2c3)

C. log_bc+ log_ab = log_ac

D. \(\frac{1}{{{{\log }_b}c}} = \frac{{{{\log }_a}c}}{{{{\log }_a}b}}\)

A. - 6

B. - 4

C. - 2

D. - 1

A. 16

B. 6

C. 13

D. 3

A. T = 16

B. T = 15

C. \(T = \frac{{27}}{2}\)

D. T = 22

A. T = 21

B. T = 12

C. T = 13

D. T = 7

A. 3

B. 12

C. \(\frac{3}{4}\)

D. \(\frac{4}{3}\)

A. - 18

B. 12

C. 18

D. - 12

A. \(A\; = \;2\left( {1 + \sqrt 2 } \right)\)

B. \(A\; = \;1\; + \sqrt 2 \)

C. \(A\; = -2(1 + \sqrt 2) \)

D. \(A\; = 3(1 + \sqrt 2) \)

A. \(A=\frac{3}{2}{\log _2}x\)

B. \(A=-\frac{1}{2}{\log _2}x\)

C. \(A=2{\log _2}x\)

D. \(A=\frac{2}{3}{\log _2}x\)

A. \(A=\frac{3}{2}{\log _2}x\)

B. \(A=-\frac{1}{2}{\log _2}x\)

C. \(A={\log _2}x\)

D. \(A=\frac{2}{3}{\log _2}x\)

A. \(A={ - \sqrt 2 }\)

B. \(A={ - 2\sqrt 2 }\)

C. \(A = \frac{{ - \sqrt 2 }}{2}\)

D. \(A = \frac{{ - \sqrt 2 }}{4}\)

A. \(A={\log _2}a\)

B. \(A=\frac{{13}}{6}{\log _2}a\)

C. \(A= \frac{3}{2}{\log _2}a\)

D. \(A= \frac{2}{3}{\log _2}a\)

A. \(x=\sqrt[4]{{{a^3}b}}\)

B. \(x = \sqrt[4]{{a{b^3}}}\)

C. \(x = \sqrt[4]{{{a^3}{b^3}}}\)

D. \(x = \sqrt[4]{{ab}}\)

A. x = 8ab

B. x = a4+ b2

C. \(x = \sqrt {{a^2}b} \)

D. x = a4b2

A. P = 108

B. P = 13

C. P =31

D. P = 30

A. \(A = \frac{{17}}{5}\)

B. \(A= \frac{{37}}{{10}}\)

C. \(A = \frac{{21}}{5}\)

D. \(A= \frac{{39}}{{10}}\)

A. \(A=\frac{1}{4}\)

B. \(A=\frac{1}{3}\)

C. \(A=\frac{1}{2}\)

D. \(A=\frac{3}{4}\)

A. \(A=\frac{4}{3}\)

B. \(A=\frac{3}{4}\)

C. \(A=\frac{8}{9}\)

D. \(A=\frac{9}{8}\)

A. \({\log _{\frac{1}{3}}}a =  - 2\)

B. log_a5 = 2

C. log₃5 = a

D. \({\log _{\frac{1}{{\sqrt 3 }}}}a = 2\)

A. log₂a = -2

B. log₃a = π

C. log₄a2 = -1

D. log₃a = - 0, 4

A. \(0<a<1, b>1\)

B. \(0<a<1,0<b<1\)

C. \(a>1, b>1\)

D. \(a>1,0<b<1\)

A. a=b

B. a>b

C. a<b

D. c>a>b

A. \(\begin{array}{ll} \log _{3} x<0 \Leftrightarrow 0<x<1 \end{array}\)

B. \( \log _{\frac{1}{3}} a>\log _{\frac{1}{3}} b \Leftrightarrow a>b>0 \)

C. \(\ln x>0 \Leftrightarrow x>1 \)

D. \( \log _{\frac{1}{2}} a=\log _{\frac{1}{2}} b \Leftrightarrow a=b>0\)

A. \(\log _{a} b<\log _{a} c \Leftrightarrow b<c\)

B. \(\log _{a} b>\log _{a} c \Leftrightarrow b>c\)

C. \(\log _{a} b>c \Leftrightarrow b>c\)

D. \(a^{b}>a^{c} \Leftrightarrow b>c\)

A. \(\log _{\frac{3}{4}} a<\log _{\frac{3}{4}} b \Leftrightarrow a<b\)

B. \(\log _{2}\left(a^{2}+b^{2}\right)=2 \log (a+b)\)

C. \(\log _{a^{2}+1} a \geq \log _{a^{2}+1} b \Leftrightarrow a \geq b\)

D. \(\log _{2} a^{2}=\frac{1}{2} \log _{2} a\)

A. \(\ln a b>2\)

B. \(\log _{a} e+\log _{b} e<2\)

C. \(\ln \frac{a}{b}>0\)

D. \(\ln b>\ln a\)

A. \(N>P>M\)

B. \(N>M>P\)

C. \(M>N>P\)

D. \(M>P>N\)

A. \(0<\log _{a} b<1\)

B. \(\log _{a} b>1\)

C. \(\log _{b} a<0\)

D. \(0<\log _{b} a<1\)

A. \(a>1, b>1\)

B. \(a>1,0<b<a\)

C. \(0<a<1,0<b<1\)

D. \(0<a<1, b>1\)

A. \(\sqrt[3]{\log _{x} 5}+\sqrt[3]{\log _{\frac{1}{2}} 5}<0\)

B. \(\sqrt[3]{\log _{x} 5}>\sqrt{\log _{x} \frac{1}{2}}\)

C. \(\sqrt{\log _{x} \frac{1}{2}}<\log _{5} \frac{1}{2}\)

D. \(\sqrt{\log _{x} \frac{1}{2}} \cdot \sqrt[3]{\log _{x} 5}>0\)

A. \(\left\{\begin{array}{l}a>10 \\ b<1\end{array}\right.\)

B. \(\left\{\begin{array}{l}0<a<10 \\ 0<b<1\end{array}\right.\)

C. \(\left\{\begin{array}{l}0<a<10 \\ b>1\end{array}\right.\)

D. \(\left\{\begin{array}{l}a>10 \\ 0<b<1\end{array}\right.\)

A. \(\log _{\frac{a}{b}}^{2} \frac{c}{b} ; \log _{\frac{b}{c}}^{2} \frac{a}{c} ; \log _{\frac{c}{a}}^{2} \frac{b}{a}=1\)

B. \(\log _{\frac{a}{b}}^{2} \frac{c}{b} ; \log _{\frac{b}{c}}^{2} \frac{a}{c}, \log _{c}^{2} \frac{b}{a}>1\)

C. \(\log _{\frac{a}{b}}^{2} \frac{c}{b} ; \log _{\frac{b}{c}}^{2} \frac{a}{c} ; \log _{\frac{c}{a}}^{2} \frac{b}{a}>-1\)

D. \(\log _{\frac{a}{b}}^{2} \frac{c}{b} ; \log _{\frac{b}{c}}^{2} \frac{a}{c} \log _{\frac{c}{a}}^{2} \frac{b}{a}<1\)

A. \(\log _{1999} 2000>\log _{2000} 2001\)

B. Hai số trên nhỏ hơn 1.

C. Hai số trên lớn hơn 2

D. \(\log _{1999} 2000 \geq \log _{2000} 2001\)

A. \(\frac{1}{\log _{a} b}<1<\frac{1}{\log _{b} a}\)

B. \( \frac{1}{\log _{a} b}<\frac{1}{\log _{b} a}<1\)

C. \(1<\frac{1}{\log _{a} b}<\frac{1}{\log _{b} a}\)

D. \(\frac{1}{\log _{b} a}<1<\frac{1}{\log _{a} b}\)

A. \(\log _{3} 2, \log _{3} 11, \log _{2} 3 .\)

B. \(\log _{3} 2, \log _{2} 3, \log _{3} 11\)

C. \(\log _{2} 3, \log _{3} 2, \log _{3} 11\)

D. \(\log _{3} 11, \log _{3} 2, \log _{2} 3\)

A. \(\log _{b} a>\log _{a} b\)

B. \(\log _{a} b>1\)

C. \(\log _{b} a<0\)

D. \(\log _{a} b>\log _{b} a\)

A. \(\left[\begin{array}{l}0<b<1<a \\ 0<a<1<b\end{array}\right.\)

B. \(\left[\begin{array}{l}0<a, b<1 \\ 1<a, b\end{array}\right.\)

C. \(\left[\begin{array}{l}0<b<1<a \\ 1<a, b\end{array}\right.\)

D. \(\left[\begin{array}{l}0<b, a<1 \\ 0<a<1<b\end{array}\right.\)

A. \(a^{\log _{a} b}=b\)

B. \(\log _{a} b=\log _{a} c \Leftrightarrow b=c\)

C. \(\log _{b} c=\frac{\log _{a} c}{\log _{a} b}\)

D. \(\log _{a} b>\log _{a} c \Leftrightarrow b>c\)

A. \(\log _{a} b>\log _{a} c \Leftrightarrow b<c\)

B. \(a^{\sqrt{2}}<a^{\sqrt{3}}\)

C. \(\log _{a} b<\log _{a} c \Leftrightarrow b>c\)

D. \(\log _{a} b>0 \Leftrightarrow b<1\)

A. \(\log _{x} 5 \leq \log _{x} 4\)

B. \(\log _{x} 5>\log _{x} 6\)

C. \(\log _{5} x=\log _{x} 5\)

D. \(\log _{5} x>\log _{6} x\)

A. \(z>x>t>y\)

B. \(z>y>t>x\)

C. \(y \geqslant z>x>t\)

D. \(z>y>x>t\)

A. \(3^{\log _{3} 4}\)

B. \(3^{2 \log _{3} 2}\)

C. \(\left(\frac{1}{4}\right)^{\log _{2} 5}\)

D. \(\left(\frac{1}{16}\right)^{\log _{0,5} 2}\)

A. \(P=2 \ln ^{2} a+1\)

B. \(P=2 \ln ^{2} a+2\)

C. \(P=2 \ln ^{2} a\)

D. \(P=\ln ^{2} a+2\)

A. P=2019

B. P=2020

C. P=2017

D. P=2016