For this case we must solve the following equation:
[tex]81 ^ x = 27^{x + 2}[/tex]
We rewrite:
[tex]81 = 3 ^ 4\\27 = 3 ^ 3[/tex]
Then, replacing:
[tex]3^{4x} = 3^{3 (x + 2)}[/tex]
For the bases to be equal then it must be fulfilled that:
[tex]4x = 3 (x + 2)\\4x = 3x + 6\\4x-3x = 6\\x = 6[/tex]
Answer:
[tex]x = 6[/tex]
Option D
