Answer:
[tex]x=\frac{35}{9} .[/tex]
Step-by-step explanation:
[tex](3\sqrt{3})^{-x+1} =\frac{1}{3}*27^{x-5}\\( \sqrt{3^2*3}) ^{1-x}=\frac{1}{3} *((3)^3)^{x-5}\\(\sqrt{27} )^{1-x}=\frac{1}{3}*3^{3*(x-5)}\\ (\sqrt{3^3})^{1-x} =\frac{1}{3}*3^{3x-15}\\ 3^{\frac{3 }{2}*(1-x)}=\frac{1}{3}*3^{3x-15}\ |*3\\ 3*3^{\frac{3}{2}-\frac{3}{2}x}=3^{3x-15}\\ 3^{1+1,5-1,5}=3^{3x-15}\\ 3^{2,5-1,5x}=3^{3x-15}\ \ \ \ \Rightarrow\\2,5-1,5x=3x-15\\4,5x =17,5\ |*2\\9x=35\ |:9\\x=\frac{35}{9}.[/tex]
