Answer:
[tex]x = \frac{1}{4}\\[/tex]
Step-by-step explanation:
Given:
[tex]27^{2x} = (\frac{1}{9})^{x-1}\\[/tex]
Rewriting your equation:
[tex](\frac{1}{27})^{-2x} = (\frac{1}{9})^{x-1} \\ ((\frac{1}{3})^3)^{-2x} = ((\frac{1}{3})^2)^{x-1} \\ (\frac{1}{3})^{-6x} = (\frac{1}{3})^{2(x-1)}[/tex]
Disregard same bases:
[tex]-6x = 2(x -1)[/tex]
Solve for [tex]x[/tex]:
[tex]-6x = 2x -2 \\ -8x = -2 \\ x = \frac{1}{4}[/tex]
