1°
[tex]( \sqrt[4]{3} )^{x}= \sqrt[3]{9} [/tex]
[tex](3^{ \frac{1}{4} })^{x}= \sqrt[3]{3^2} [/tex]
[tex](3^{ \frac{1}{4} })^{x}= 3^{ \frac{2}{3} }[/tex]
[tex]\not{3}^{ \frac{1x}{4} }=\not{3}^{ \frac{2}{3} }[/tex]
[tex] \frac{1x}{4} = \frac{2}{3} ~\to~3x=8~\to~\boxed{x= \frac{8}{3}} [/tex]
2°
[tex]8^{x}=0.25\\8^{x}= \frac{25}{100} \\8^{x}= \frac{1}{4} [/tex]
[tex](2^3)^{x}=2^{-2}\\\not{2}^{3x}=\not{2}^{-2}[/tex]
[tex]3x=-2~\to \boxed{x= \frac{-2}{3}} [/tex]
3°
[tex]( \sqrt[6]{2} )^{x}=0.5\\( \sqrt[6]{2} )^{x}= \frac{5}{10} [/tex]
[tex]( \sqrt[6]{2} )^{x}= \frac{1}{2} [/tex]
[tex]2^{ \frac{1x}{6} }=2^{-1}[/tex]
[tex]\boxed{x=-6}[/tex]
