Trắc nghiệm Lôgarit Toán Lớp 12

A. \({\log _b}a\; + \;{\log _a}b < 0\)

B. \({\log _b}a\; + \;{\log _a}b = 0\)

C. \({\log _b}a\; + \;{\log _a}b > 0\)

D. \({\log _b}a\; + \;{\log _a}b \ge  2\)

A. Chỉ có (I), (II) và (III)

B. Chỉ có (II), (III) và (IV)

C. Chỉ có (II) và (IV)

D. Chỉ có (I) và (III)

A. \({\left( {\frac{1}{3}} \right)^{\rm{\pi }}},{\left( {\frac{1}{3}} \right)^{\sqrt 2 }},{\left( {\frac{1}{3}} \right)^0},{\left( {\frac{1}{3}} \right)^{ - 1}}\)

B. \({\left( {\frac{1}{3}} \right)^{ - 1}},{\left( {\frac{1}{3}} \right)^0},{\left( {\frac{1}{3}} \right)^{\rm{\pi }}},{\left( {\frac{1}{3}} \right)^{\sqrt 2 }}\)

C. \({\left( {\frac{1}{3}} \right)^{ - 1}},{\left( {\frac{1}{3}} \right)^0},{\left( {\frac{1}{3}} \right)^{\sqrt 2 }},{\left( {\frac{1}{3}} \right)^{\rm{\pi }}}\)

D. \({\left( {\frac{1}{3}} \right)^0},{\left( {\frac{1}{3}} \right)^{ - 1}},{\left( {\frac{1}{3}} \right)^{\rm{\pi }}},{\left( {\frac{1}{3}} \right)^{\sqrt 2 }}\)

A. \(\sqrt {1 - {a^2}} \)

B. \({b^a}^2\)

C. \(2{\log _b}\left( {1 - {b^{\frac{a}{2}}}} \right)\)

D. \(\frac{1}{2}{\log _b}\left( {1 - {b^{2a}}} \right)\)

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

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

C. 2

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

A. \(m = {n^3}\)

B. \(m = \frac{1}{{{n^3}}}\)

C. \(m = \sqrt[3]{n}\)

D. \(m = \frac{1}{{\sqrt[3]{n}}}\)

A. pq

B. \(\frac{{3p + q}}{5}\)

C. \(\frac{{3p + q}}{{1 + 3pq}}\)

D. \(\frac{{1 + 3pq}}{{p + q}}\)

A. \(a = \frac{{2b}}{3}\)

B. \(a = \frac{{b}}{2}\)

C. \(a =- \frac{{b}}{2}\)

D. \(a = \frac{{3b}}{2}\)

A. \(\frac{1}{{{{\log }_x}60}}\)

B. \(\frac{1}{{{{\log }_3}x\)

C. \(\frac{1}{{\left( {{{\log }_3}x} \right).\left( {{{\log }_4}x} \right).\left( {{{\log }_5}x} \right)}}\)

D. \(\frac{1}{{{{\log }_3}x + {{\log }_4}x + {{\log }_5}x}}\)

A. \(\frac{1}{{10}}\)

B. \(-\frac{1}{{10}}\)

C. 2

D. - 2

A. \(\frac{1}{8}\)

B. 1

C. 8

D. 6

A. 5log3

B. 3 - 3log2 

C. 100log1,25 

D. (log25)(log5)

A. \(y\; = \;3\sqrt {u}.v \)

B. \(y = 3{u^2}v\)

C. \(y\; = \;3\; + \;\sqrt u \; + \;v\;\)

D. \(y\; = \;{\left( {\sqrt {uv} } \right)^3}\)

A. \(x = {\log _2}{y^3}\)

B. \(x = \frac{1}{3}{2^y}\)

C. \(x = \frac{1}{3}{\log _2}y\)

D. \(x = \frac{1}{3}{\log _y}2\)

A. P = 3 + a - 2b

B. P = 3 + a - b2

C. \(P\; = \;\frac{{3a}}{{2b}}\)

D. \(P\; = \;\frac{{3a}}{{{b^2}}}\)

A. \(P\; = \;6{\log _3}a.{\log _3}b\)

B. \(P\; = \;2{\log _3}a\; + \;3{\log _3}b\)

C. \(P\; = \;\frac{1}{2}{\log _3}a\; + \;\frac{1}{3}{\log _3}b\)

D. \(P\; = \;{\left( {{{\log }_3}a} \right)^2}.{\left( {{{\log }_3}b} \right)^3}\)

A. 1

B. \({\log _7}10\)

C. 7

D. \(\log 7\)

A. - 2

B. 2

C. \( - 3{\log _a}5\)

D. \( 3{\log _a}5\)

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

B. 1

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

D. 4

A. - 3

B. - 2

C. 2

D. 3

A. \(\frac{{\log \frac{S}{P}}}{{\log \left( {1 + k} \right)}}\)

B. \(\log \frac{S}{P} + \log \left( {1 + k} \right)\)

C. \(\log \frac{S}{{P\left( {1 + k} \right)}}\)

D. \(\frac{{\log S}}{{\log \left[ {P\left( {1 + k} \right)} \right]}}\)

A. \(P = 1 + \frac{{ab}}{{1 + a}}\)

B. \(P = 1 + \frac{{ab}}{{1 + b}}\)

C. \(P = \frac{{2 + b + ab}}{{1 + b}}\)

D. \(P = \frac{{2 + a + ab}}{{1 + a}}\)

A. 1

B. \(\log \frac{x}{y}\)

C. \(\frac{{\log y}}{x}\)

D. \(\log \frac{{{a^2}y}}{{{d^2}x}}\)

A. \(y=2x+3\)

B. \(y=8x^2\)

C. \(y=x^2+8\)

D. \(y=3x^2\)

A. \(u=a \frac{-1}{1-\log _{a} v}\)

B. \(u=a \frac{1}{1+\log _{a} t}\)

C. \(u=a \frac{1}{1+\log _{a} v} \)

D. \(u=a \frac{1}{1-\log _{a} v}\)

A. \(\frac{a+c}{3 a b+3}\)

B. \(\frac{a+c+2}{3 a b}\)

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

D. \(\frac{a+c+2}{3 a b+3}\)

A. \(\log \frac{a+b}{4} =\frac{1}{2}(\log a+\log b)\)

B. \(2(\log a+\log b)=\log (14 a b)\)

C. \(\log (a+b)=2(\log a+\log b)\)

D. \(\log (a+b)-4=\frac{1}{2}(\log a+\log b)\)

A. \(\log \left(\frac{2 a+3 b}{5}\right)=\frac{1}{2}(\log a+\log b)\)

B. \(\frac{1}{4} \log (2 a+3 b)=3 \log a+2 \log b\)

C. \(\log \sqrt{2 a+3 b}=\log \sqrt{a}+2 \log \sqrt{b}\)

D. \(\log \left(\frac{2 a+3 b}{4}\right)=\frac{1}{2}(\log a+\log b)\)

A. \(\sqrt[3]{\log _{a} b}\)

B. \(\sqrt{\log _{a} b}\)

C. \(\left(\sqrt{\log _{a} b}\right)^{3}\)

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

A. \(y=q^{2}-p r\)

B. \(y=\frac{p+r}{2 a}\)

C. \(y=2 q-p -r\)

D. \(y=2 q-p r\)

A. 5

B. 2

C. 0

D. \(1\over 2\)

A. \(a^{3}=b^{2}\)

B. \(x=a b\)

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

D. \(a=b^{2} \,\,hoặc \,\,a^{3}=b^{2}\)

A. 3

B. 1

C. 2

D. 0

A. \(\log _{b+c} a+\log _{c-b} a=2 \log _{b+c} a \cdot \log _{c-b} a\)

B. \(\log _{b+c} a+\log _{c-b} a>2 \log _{b+c} a \cdot \log _{c-b} a\)

C. \(\log _{b+c} a+\log _{c-b} a<2 \log _{b+c} a \cdot \log _{c-b} a\)

D. \(\log _{b+c} a+\log _{c-b} a=\log _{b+c} a \cdot \log _{c-b} a\)

A. -n

B. 3n

C. -3n

D. 2n

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

B. \(\log _{a^{2}}(a b)=\frac{1}{4} \log _{a} b\)

C. \(\log _{a^{2}}(a b)=2+2 \log _{a} b\)

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

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. \(a^{c}=b^{d} \Leftrightarrow \ln \left(\frac{a}{b}\right)=\frac{c}{d}\)

B. \(a^{c}=b^{d} \Leftrightarrow \frac{\ln a}{\ln b}=\frac{d}{c}\)

C. \(a^{c}=b^{d} \Leftrightarrow \frac{\ln a}{\ln b}=\frac{c}{d}\)

D. \(a^{c}=b^{d} \Leftrightarrow \ln \left(\frac{a}{b}\right)=\frac{d}{c}\)

A. \(a^{\ln b}=b^{\ln a}\)

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

C. \(\ln \left(\frac{a}{b}\right)=\frac{\ln a}{\ln b}\)

D. \(\ln \sqrt{a b}=\frac{1}{2}(\ln \sqrt{a}+\ln \sqrt{b})\)

A. \(\log _{m} 8 m=\frac{3+a}{a}\)

B. \(\log _{m} 8 m=(3-a) a \)

C. \(\log _{m} 8 m=\frac{3-a}{a}\)

D. \(\log _{m} 8 m=(3+a) a\)

A. \(P=\frac{\sqrt{3}}{3}\)

B. \(P=3 \sqrt{3}\)

C. \(P=27\)

D. \(P=\frac{1}{3}\)

A. log_ab < 1 < log_ba

B. 1 < log_ab < log _ba

C. log_ab < log_ba < 1

D. log_ba < 1< log_ab 

A. 2a + 2ab

B. a + ab

C. 3a + ab

D. 2a + ab

A. \( {\log _2}3 = \frac{{a - 2}}{{1 - 2a}}\)

B. \( {\log _2}3 = \frac{{a - 2}}{{2a-1}}\)

C. \( {\log _2}3 = \frac{{a +2}}{{ 2a-1}}\)

D. \( {\log _2}3 = \frac{{a - 1}}{{1 - 2a}}\)

A. log_ab < 1 < log_ba

B. 1 < log_ab < log_ba

C. log_ab < log_ba < 1

D. log_ba < 1< log_ab

A. \({\log _{ab}}\frac{a}{b} = \frac{{1 + {{\log }_a}b}}{{1 - {{\log }_a}b}}\)

B. \({\log _{ab}}\frac{a}{b} = \frac{{1 - {{\log }_a}b}}{{1 + {{\log }_a}b}}\)

C. \({\log _{ab}}\frac{a}{b} = \frac{{1 +{{\log }_a}b}}{{1 - {{\log }_a}b}}\)

D. \({\log _{ab}}\frac{a}{b} = \frac{{1 + {{\log }_a}b}}{{1 - {{\log }_b}b}}\)

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

B. \({\log _{{a^2}}}ab = \frac{1}{4}{\log _a}b\)

C. \({\log _{{a^2}}}ab = 2 + 2{\log _a}b\)

D. \({\log _{{a^2}}}ab = \frac{1}{2} + \frac{1}{2}{\log _a}b\)

A. \({\log _{\sqrt 3 }}50 = \frac{{a + b + 1}}{2}\)

B. \({\log _{\sqrt 3 }}50 = \frac{{a + b - 1}}{2}\)

C. \({\log _{\sqrt 3 }}50 = 2a + 2b + 2\)

D. \({\log _{\sqrt 3 }}50 = 2a + 2b - 2\)

A. \({\log _{15}}30 = \frac{{1 + q}}{{p + q}}\)

B. \({\log _{15}}30 = \frac{{1 + p}}{{p + q}}\)

C. \({\log _{15}}30 = \frac{{p + q}}{{p+1}}\)

D. \({\log _{15}}30 = \frac{{p + q}}{{q+1}}\)

A. - 1

B. - 2

C. 1

D. \({\log _2}\sqrt 3  - 1\)