Question

Need help!!! Thanks!!! Pre-Cal 27^(2x) = (1/9)^(x-1)

Answer 1

Answer:

$x = \frac{1}{4}$

Step-by-step explanation:

Given:

$27^{2x} = (\frac{1}{9})^{x-1}$

Rewriting your equation:

$(\frac{1}{27})^{-2x} = (\frac{1}{9})^{x-1} \\ ((\frac{1}{3})^3)^{-2x} = ((\frac{1}{3})^2)^{x-1} \\ (\frac{1}{3})^{-6x} = (\frac{1}{3})^{2(x-1)}$

Disregard same bases:

$-6x = 2(x -1)$

Solve for $x$:

$-6x = 2x -2 \\ -8x = -2 \\ x = \frac{1}{4}$