Cho a, b, c là các số dương và a, b khác 1. Khẳng định nào sau đây là sai?

A. −3

B. \[\frac{1}{3}\]

C. \[ - \frac{1}{3}\]

D. 3

A. \[\frac{1}{5}\]

B. \[ - \frac{1}{5}\]

C. 5

D. −5

A. \[{\rm{T}} = - \frac{2}{5}\]

B. \[{\rm{T}} = \frac{2}{5}\]

C. \[{\rm{T}} = \frac{2}{3}\]

D. \[{\rm{T}} = - \frac{2}{3}\]

A. \[{\rm{lo}}{{\rm{g}}_{{{\rm{a}}^{\rm{3}}}}}\left( {\frac{{\rm{a}}}{{\sqrt {\rm{b}} }}} \right){\rm{ = }}\frac{{\rm{1}}}{{\rm{3}}}\left( {{\rm{1 + }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{lo}}{{\rm{g}}_{\rm{a}}}{\rm{b}}} \right){\rm{.}}\]

B. \[{\mathop{\rm lo}\nolimits} {{\rm{g}}_{{{\rm{a}}^{\rm{3}}}}}\left( {\frac{{\rm{a}}}{{\sqrt {\rm{b}} }}} \right) = \frac{1}{3}\left( {1 - 2{\mathop{\rm lo}\nolimits} {{\rm{g}}_{\rm{a}}}{\rm{b}}} \right).\]

C. \[{\mathop{\rm l}\nolimits} {\rm{o}}{{\rm{g}}_{{{\rm{a}}^{\rm{3}}}}}\left( {\frac{{\rm{a}}}{{\sqrt {\rm{b}} }}} \right) = \frac{1}{3}\left( {1 - \frac{1}{2}{\mathop{\rm l}\nolimits} {\rm{o}}{{\rm{g}}_{\rm{a}}}{\rm{b}}} \right).\]

D. \[{\log _{{{\rm{a}}^{\rm{3}}}}}\left( {\frac{{\rm{a}}}{{\sqrt {\rm{b}} }}} \right) = 3\left( {1 - \frac{1}{2}{\mathop{\rm lo}\nolimits} {{\rm{g}}_{\rm{a}}}{\rm{b}}} \right).\]

A. Nếu \[0 < {{\rm{x}}_1} < {{\rm{x}}_2}\]thì \[{\log _a}{{\rm{x}}_1} < {\log _a}{{\rm{x}}_2}\].

B. Nếu \[{\log _a}{\rm{x}} < 1\] thì 0 < x < a

C. Nếu \[{\rm{lo}}{{\rm{g}}_{\rm{a}}}{\rm{x}} > 0\] khi x > 1

D. Nếu \[{\rm{lo}}{{\rm{g}}_{\rm{a}}}{\rm{x > lo}}{{\rm{g}}_{\rm{a}}}{{\rm{x}}^{\rm{2}}}\] thì x > 1

A. \[{\rm{lo}}{{\rm{g}}_{\rm{a}}}{{\rm{a}}^{\rm{b}}}{\rm{ = }}{{\rm{a}}^{\rm{b}}}\]

B. \[{\rm{lo}}{{\rm{g}}_{\rm{a}}}{{\rm{a}}^{\rm{b}}}{\rm{ = a}}\]

C. \[{{\rm{a}}^{{\rm{lo}}{{\rm{g}}_{\rm{a}}}{\rm{b}}}}{\rm{ = }}{{\rm{a}}^{\rm{b}}}\]

D. \[{{\rm{a}}^{{\rm{lo}}{{\rm{g}}_{\rm{a}}}{\rm{b}}}}{\rm{ = lo}}{{\rm{g}}_{\rm{a}}}{{\rm{a}}^{\rm{b}}}\]