Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
Given:
[tex]81^x = 27^{x +2}[/tex]
Solving for [tex]x[/tex]:
[tex]81^x = 27^{x +2} \\ 81^x = (81^{\frac{3}{4}})^{x +2} \\ 81^x = 81^{\frac{3}{4}(x +2)} \\ x = \frac{3}{4}(x +2) \\ x = \frac{3}{4}x +\frac{3}{4}(2) \\ x = \frac{3}{4}x +\frac{3}{2} \\ x -\frac{3}{4}x = \frac{3}{2} \\ \frac{4}{4}x -\frac{3}{4}x = \frac{3}{2} \\ \frac{1}{4}x = \frac{3}{2} \\ x = \frac{3}{2} \cdot 4 \\ x = \frac{12}{2} \\ x = 6[/tex]
