[tex]\displaystyle \bf\\
3^{x+1} = 9^{ \sqrt{x} }\\\\
3^{x+1} = \Big(3^2\Big)^{ \sqrt{x} }\\\\
3^{x+1} = 3^{2 \sqrt{x} }\\\\
x+1 = 2\sqrt{x} ~~~\Big| ~Ridicam~ la ~puterea ~ a~ doua.\\\\
(x+1)^2=(2\sqrt{x})^2\\\\
x^2+2x+1 = 4x\\\\
x^2+2x-4x+1 = 0\\\\
x^2 -2x+1 = 0\\\\
(x-1)^2 = 0\\\\
x-1 = 0\\\\
\boxed{\bf x = 1 } ~~~\text{(Radacina dubla)} [/tex]
