Question

solve for x:
27^(2x)=(1/9)^(x-3)

Answer 1

$27^{2x}=\left(\dfrac{1}{9}\right)^{x-3}\\\\(3^3)^{2x}=\left(\dfrac{1}{3^2}\right)^{x-3}\\\\3^{3\cdot2x}=(3^{-2})^{x-3}\\\\3^{6x}=3^{-2(x-3)}\\\\3^{6x}=3^{-2x+6}\iff6x=-2x+6\ \ \ |add\ 2x\ to\ both\ sides\\\\8x=6\ \ \ |divide\ both\ sides\ by\ 8\\\\x=\dfrac{6}{8}\\\\\boxed{x=\frac{3}{4}}$

Answer 2

$27^{2x}=\left(\dfrac{1}{9}\right)^{x-3}\\ (3^3)^{2x}=(3^{-2})^{x-3}\\ 3^{6x}=3^{-2x+6}\\ 6x=-2x+6\\ 8x=6\\ x=\dfrac{6}{8}=\dfrac{3}{4}$