Trắc nghiệm Lôgarit Toán Lớp 12

A. x<y      

B. x>y     

C. x≤y

D. x≥y

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. 0

B. 1

C. 2

D. 3

A. \( {\log _a}b.lo{g_b}a = 1\)

B. \( \ln \frac{x}{{\sqrt y }} = \ln x - \frac{1}{2}\ln y\)

C. \( {\log _a}x + {\log _{\sqrt[3]{a}}}y = {\log _a}\left( {x{y^3}} \right)\)

D. \( {\log _a}\left( {x + y} \right) = {\log _a}x + {\log _a}y\)

A. \(\ln {\left( {ab} \right)^2} = \ln \left( {{a^2}} \right) + \ln \left( {{b^2}} \right)\)

B. \( \ln \left( {\sqrt {ab} } \right) = \frac{1}{2}\left( {\ln a + \ln b} \right)\)

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

D. \( \ln {\left( {\frac{a}{b}} \right)^2} = \ln \left( {{a^2}} \right) - \ln \left( {{b^2}} \right)\)

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

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

C. \( \ln \left( {a{b^n}} \right) = \ln a + n\ln b\)

D. \( \ln {e^2} = e\)

A. \(x=e\)

B. \(x = ( − 1 ) ^e\)

C. \( x = \frac{1}{e}\)

D. \(x=\sqrt e\)

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

B. \( \log \left( {a + 1} \right) + \log b = 1\)

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

D. \( 5\log \left( {a + 2b} \right) = \log a - \log b\)

A. 18

B. 20

C. 19

D. 21

A. \(x=3a+5b\)

B. \(x=5a+3b\)

C. \(x=a^5+b^3\)

D. \(x=a^5b^3\)

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

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

C. \(\frac{5}{2}\)

D. \(\frac{7}{2}\)

A. \( \frac{a}{b} = \frac{{3 + \sqrt 6 }}{4}\)

B. \( \frac{a}{b} =7- 2\sqrt 6 \)

C. \( \frac{a}{b} =7+2\sqrt 6 \)

D. \( \frac{a}{b} =- 2\sqrt 6 \)

A. \( {\log _{12}}80 = \frac{{2{a^2} - 2ab}}{{ab + b}}\)

B. \( {\log _{12}}80 = \frac{{a + 2ab}}{{ab}}\)

C. \( {\log _{12}}80 = \frac{{a + 2ab}}{{ab + b}}\)

D. \( {\log _{12}}80 = \frac{{2{a^2} - 2ab}}{{ab}}\)

A. \( {\log _3}90 = \frac{{a - 2b + 1}}{{b + 1}}\)

B. \( {\log _3}90 = \frac{{a+2b -1}}{{b - 1}}\)

C. \( {\log _3}90 = \frac{{2a-b+ 1}}{{a + 1}}\)

D. \( {\log _3}90 = \frac{{2a+b - 1}}{{a- 1}}\)

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

B. \( \frac{{3}}{4a}\)

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

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

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

B. \( \frac{{2}}{{5(a - 1)}}\)

C. \( \frac{{5}}{{2a - 2}}\)

D. \( \frac{{5}}{{2a + 1}}\)

A. -2

B. -4

C. -6

D. -8

A. \( 8 - 5\sqrt 3 \)

B. \( \frac{{13 - 4\sqrt 3 }}{{11}}\)

C. \(5\sqrt3 -8\)

D. \( \frac{ {4\sqrt 3-13 }}{{11}}\)

A. \( {a^2}{p^4}\)

B. \(4p+2\)

C. \(4p+2a\)

D. \(p^4+2a\)

A. \( P = \frac{{\sqrt 2 }}{2}\)

B. \( P = \frac{{4-\sqrt 2 }}{2}\)

C. \( P = \frac{{3\sqrt 2 }}{2}\)

D. \( P = 2\sqrt2\)

A. \(3+2a\)

B. \(a^2\)

C. \(3a^2\)

D. \(a^2+3\)

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

B. \( \frac{{2a - 1}}{{a - 2}}\)

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

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

A. \( {\log _6}45 = \frac{{2{a^2} - 2ab}}{{ab}}\)

B. \( {\log _6}45 = \frac{{2{a^2} - 2ab}}{{ab+b}}\)

C. \( {\log _6}45 = \frac{{{a} + 2ab}}{{ab+b}}\)

D. \( {\log _6}45 = \frac{{{a} + 2ab}}{{ab}}\)

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

B. \( P = \frac{{a + b + 4}}{a}\)

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

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

A. a>1,0<b<1

B. 0<a<1,0<b<1

C. 0<a<1,b>1

D. a>1,b>1

A. \(2{\log _2}\frac{a}{b}\)

B. \( \frac{1}{2}{\log _2}\frac{a}{b}\)

C. \( {\log _2}a - 2{\log _2}b\)

D. \( {\log _2}a - {\log _2}\left( {2b} \right)\)

A. \(2 log a + log b\)

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

C. \(2(loga+logb)\)

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

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

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

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

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

A. \( 2b - 3a = 2.\)

B. \( {b^3} - {a^3} = 4.\)

C. \(b^2=4a^3\)

D. \( 2b - 3a = 4.\)

A. \( {m^2} - {n^2} = 312\)

B. \( {m^2} - {n^2} = 313\)

C. \( {m^2} - {n^2} = 314\)

D. \( {m^2} - {n^2} = 315\)

A. \( P = {\log _2}{\left( {\frac{a}{b}} \right)^2}\)

B. \( P = {\log _2}\left( {\frac{{2a}}{{{b^2}}}} \right)\)

C. \( P = {\log _2}\left( {2a{b^2}} \right)\)

D. \( P = {\log _2}{\left( {ab} \right)^2}\)

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

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

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

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

A. 0<a<1

B. 0<a<3

C. a>3           

D. a>1

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. \( {\log _a}b = 0\)

B. \( {\log _a}b > 0\)

C. \( {\log _a}b < 0\)

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

A. \( {\log _a}b > {\log _a}c\)

B. \({\log _a}b < {\log _a}c\)

C. \( {\log _a}b < {\log _b}c\)

D. \( {\log _a}b > {\log _c}b\)

A. 1

B. 2

C. 3

D. 4

A. \(\frac{5}{6}\)

B. \(\frac{7}{6}\)

C. \(\frac{1}{6}\)

D. \(5\)

A. \( {\log _{{2^n}}}a = {\log _{{a^n}}}2.\)

B. \( {\log _{{2^n}}}a = \frac{n}{{{{\log }_2}a}}.\)

C. \( {\log _{{2^n}}}a = \frac{1}{{n{{\log }_a}2}}.\)

D. \({\log _{{2^n}}}a = - n{\log _a}2.\)

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

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

C. \( {\log _{{a^n}}}b = {\log _a}\sqrt[n]{b}\)

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

A. \( {\log _a}\frac{x}{y} = {\log _a}x + {\log _a}y\)

B. \( {\log _a}\frac{x}{y} = {\log _a}\left( {x - y} \right)\)

C. \( {\log _a}\frac{x}{y} = {\log _a}x - {\log _a}y\)

D. \( {\log _a}\frac{x}{y} = \frac{{{{\log }_a}x}}{{{{\log }_a}y}}\)

A. \( 2 - {\log _a}b\)

B. \( 2 +{\log _a}b\)

C. \( 1+2 {\log _a}b\)

D. \( 2 {\log _a}b\)

A. 1

B. 2

C. 3

D. 4

A. \( {\log _{{a^3}}}\left( {\frac{a}{{\sqrt b }}} \right) = \frac{1}{3}\left( {1 + \frac{1}{2}{{\log }_a}b} \right).\)

B. \( {\log _{{a^3}}}\left( {\frac{a}{{\sqrt b }}} \right) = \frac{1}{3}\left( {1 - 2{{\log }_a}b} \right).\)

C. \({\log _{{a^3}}}\left( {\frac{a}{{\sqrt b }}} \right) = \frac{1}{3}\left( {1 - \frac{1}{2}{{\log }_a}b} \right).\)

D. \( {\log _{{a^3}}}\left( {\frac{a}{{\sqrt b }}} \right) = 3\left( {1 - \frac{1}{2}{{\log }_a}b} \right).\)

A. -4

B. -6

C. -8

D. -10

A. 3

B. 4

C. 5

D. 6

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

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

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

D. \( {\log _{{a^n}}}b = n{\log _a}b\)

A. \( {\log _a}c = {\log _a}b.{\log _b}c\)

B. \( {\log _a}c = \frac{1}{{{{\log }_c}a}}\)

C. \( {\log _a}b.{\log _b}a = 1\)

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

A. \( {\log _a}b.{\log _b}c = {\log _a}c\)

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

C. \({\log _a}b = {\log _c}b - {\log _c}a\)

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

A. \( {\log _2}\frac{{2\sqrt[3]{a}}}{{{b^3}}} = 1 + \frac{1}{3}{\log _2}a - \frac{1}{3}{\log _2}b\)

B. \( {\log _2}\frac{{2\sqrt[3]{a}}}{{{b^3}}} = \frac{1}{3}{\log _2}a +\frac{1}{3}{\log _2}b\)

C. \( {\log _2}\frac{{2\sqrt[3]{a}}}{{{b^3}}} = 1 + \frac{1}{3}{\log _2}a +\frac{1}{3}{\log _2}b\)

D. \( {\log _2}\frac{{2\sqrt[3]{a}}}{{{b^3}}} = 1 + \frac{1}{3}{\log _2}a -3{\log _2}b\)