[tex]3\times9^{x+1}=27^{x-1}\\\\3\times(3^2)^{x+1}=(3^3)^{x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\3\times3^{2(x+1)}=3^{3(x-1)}\\\\3\times3^{2x+2}=3^{3x-3}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\3^{1+2x+2}=3^{3x-3}\\\\3^{2x+3}=3^{3x-3}\iff2x+3=3x-3\qquad\text{subtract 3 from both sides}\\\\2x=3x-6\qquad\text{subtract 3x from both sides}\\\\-x=-6\to\boxed{x=6}[/tex]
