cho x, y là 2 số dương ; m,n là hai số thực tùy ý :

Lời giải
a) Đúng, b) Đúng, c) Sai, d) Sai
a) ${\left(x^m\right)}^n={\left(x^n\right)}^m$ » Chọn ĐÚNG
b) $x^{2m}={\left(x^m\right)}^2$ » Chọn ĐÚNG
c) ${\log }_{5}25x=5+{\log }_{5}x$
Ta có ${\log }_{5}25x={\log }_{5}25+{\log }_{5}x={\log }_5{5}^2+{\log }_{5}x=2+{\log }_{5}x$
» Chọn SAI.
d) ${\log }_{\sqrt{3}}x+{\log }_{\frac{1}{3}}\left(3x^{3}y\right)+{\log }_9\left(3y^3\right)=1$
${\log }_{\sqrt{3}}x+{\log }_{\frac{1}{3}}\left(3x^{3}y\right)+{\log }_9\left(3y^3\right)$
$={\log }_{3^{\frac{1}{2}}}x+{\log }_{3^{-1}}3+{\log }_{3^{-1}}{x}^3+{\log }_{3^{-1}}y+{\log }_{3^2}3+{\log }_{3^2}{y}^3$
$=2{\log }_{3}x-1-3{\log }_{3}x-{\log }_{3}y+\frac{1}{2}+\frac{3}{2}{\log }_{3}y$
$=-{\log }_{3}x+\frac{1}{2}{\log }_{3}y-\frac{1}{2}$
» Chọn SAI
a) a) ${\left(x^m\right)}^n={\left(x^n\right)}^m$ » Chọn ĐÚNG
b) b) $x^{2m}={\left(x^m\right)}^2$ » Chọn ĐÚNG
c) c) ${\log }_{5}25x=5+{\log }_{5}x$
Ta có ${\log }_{5}25x={\log }_{5}25+{\log }_{5}x={\log }_5{5}^2+{\log }_{5}x=2+{\log }_{5}x$
» Chọn SAI.
d) d) ${\log }_{\sqrt{3}}x+{\log }_{\frac{1}{3}}\left(3x^{3}y\right)+{\log }_9\left(3y^3\right)=1$
${\log }_{\sqrt{3}}x+{\log }_{\frac{1}{3}}\left(3x^{3}y\right)+{\log }_9\left(3y^3\right)$
$={\log }_{3^{\frac{1}{2}}}x+{\log }_{3^{-1}}3+{\log }_{3^{-1}}{x}^3+{\log }_{3^{-1}}y+{\log }_{3^2}3+{\log }_{3^2}{y}^3$
$=2{\log }_{3}x-1-3{\log }_{3}x-{\log }_{3}y+\frac{1}{2}+\frac{3}{2}{\log }_{3}y$
$=-{\log }_{3}x+\frac{1}{2}{\log }_{3}y-\frac{1}{2}$
» Chọn SAI