Trắc nghiệm Logarit có đáp án (Thông hiểu)

A. ${\log }_{2}16={\log }_{3}81$

B. ${\log }_{3}9=3$

C. ${\log }_{4}16={\log }_{2}8$

D. ${\log }_{2}4={\log }_{3}6$

A. ${\log }_2{a}^3=3{\log }_{2}a$

B. ${\log }_2{a}^3=\frac{1}{3}{\log }_{2}a$

C. ${\log }_2{a}^3=\frac{3}{2}\log a$

D. ${\log }_2{a}^3=3\log a$

A. $2^{{\log }_{2}3}=5^{{\log }_{3}5}$

B. $2^{{\log }_{2}3}=5^{{\log }_{5}3}$

C. $5^{{\log }_{5}3}={\log }_{2}3$

D. $2^{{\log }_{2}4}=2$

A. ${\log }_{5}6={\log }_{2}6.{\log }_{3}6$

B. ${\log }_{5}6={\log }_{5}2+{\log }_{5}3$

C. ${\log }_{5}6={\log }_{5}5.{\log }_{5}1$

D. ${\log }_{5}6={\log }_{5}2.{\log }_{5}3$

A. $T=-\frac{2}{5}$

B. $T=\frac{2}{5}$

C. $T=\frac{2}{3}$

D. $T=-\frac{2}{3}$

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

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

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

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

A. $2{\log }_a\sqrt{b}={\log }_{a}b$

B. ${\log }_a\sqrt{b}=2{\log }_{a}b$

C. ${\log }_a\sqrt{b}=\frac{1}{3}$

D. ${\log }_a\sqrt{b}=-\frac{1}{3}{\log }_{a}b$

A. ${\log }_{2}3=-{\log }_{3}2$

B. ${\log }_{3}2.{\log }_3\frac{1}{2}=1$

C. ${\log }_{2}3+{\log }_{3}2=1$

D. ${\log }_{2}3=\frac{1}{{\log }_{3}2}$

A. $2-{\log }_{a}b$

B. $2+{\log }_{a}b$

C. $1+2{\log }_{a}b$

D. $2{\log }_{a}b$

A. I=3

B. $I=\frac{1}{3}$

C. $I=-\frac{1}{3}$

D. I=-3

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. ${\log }_{2^n}a={\log }_{a^n}2$

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. 2

B. -8

C. -2

D. $\frac{1}{2}$

A. $I=-\frac{1}{3}$

B. I=-3

C. $I=\frac{1}{3}$

D. I=3

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

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

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

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

A. $e^{\ln 2}+\ln \left(e^2.\sqrt[3]{e}\right)=\frac{10}{3}$

B. $e^{\ln 2}+\ln \left(e^2.\sqrt[3]{e}\right)=\frac{13}{3}$

C. $e^{\ln 2}+\ln \left(e^2.\sqrt[3]{e}\right)=\frac{15}{3}$

D. $e^{\ln 2}+\ln \left(e^2.\sqrt[3]{e}\right)=4$

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. ${\log }_{\sqrt{a}}\left(a^2+ab\right)=4+2{\log }_{a}b$

B. ${\log }_{\sqrt{a}}\left(a^2+ab\right)=4{\log }_a(a+b)$

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

D. ${\log }_{\sqrt{a}}\left(a^2+ab\right)=1+4{\log }_{a}b$

A. a>1,0<b<1

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

C. 0<a<1, b>1

D. a>1, b>1