The answer is \(x = - \frac{4}{3}\)
\(27^{2x} = 9^{(x-3)} \\ (3^{3} )^{2x} = (3^{2}) ^{(x-3)} \\ \\ (x^{a} )^{b}= x^{a*b} \\ 3^{3*2x} =3^{2*(x-3)} \\ 3^{6x} =3^{(2x-6)}\)
Now, logarithm both sides of the equation:
\(log(3^{6x} )=log(3^{(2x-6)}) \\ \\ log (x^{a}) =a*log(x) \\ 6x*log(3)=(2x-6)*log(3)\)
Divide both sides of the equation by log(3):
\(6x=2x-6
\\ 6x-2x = -6 \\
4x = -3 \\
x = - \frac{4}{3}\)
