[tex]9\cdot 3^\big{\text{x}}=27^\big{\text{x}} \\ \\ 9\cdot 3^\big{\text{x}} ={\Big(3^\big3\Big)}^\big{\text{x}} \\ \\ 9\cdot 3^\big{\text{x}} = 3^{\big3\cdot \big{\text{x}}}\\ \\ 9\cdot 3^\big{\text{x}} = \Big(3^\big{\text{x}}\Big)^\big3 \\ \\ 9 = \dfrac{\Big(3^\big{\text{x}}\Big)^\big3}{ 3^\big{\text{x}}}\\ \\ 9 = \Big(3^\big{\text{x}}\Big)^\big2 \\ \\ 3^\big2 = \Big(3^\big2\Big)^\big{\text{x}} \\ \\ \Rightarrow\boxed{ \text{x} = 1}[/tex]
