Question

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

Answer 1

`27^(2x)=\left((1)/(9)\right)^(x-3)\\ (3^3)^(2x)=(3^(-2))^(x-3)\\ 3^(6x)=3^(-2x+6)\\ 6x=-2x+6\\ 8x=6\\ x=(6)/(8)=(3)/(4)`

Answer 2

`27^(2x)=\left((1)/(9)\right)^(x-3)\\\\(3^3)^(2x)=\left((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=(6)/(8)\\\\\boxed{x=(3)/(4)}`