2024 CCHY P1 Q8

Simplify \(2^{3x - 4} \times 9^{x - 3} = 6^{2(x - 2)}\) in the form \(\left(\frac{m \times n}{36}\right)^x = 9\), where \(m\) and \(n\) are integers.

Hence solve for \(x\), giving your answer in the simplest form \(\frac{\ln a}{\ln b}\), where \(a\) and \(b\) are integers.[5]