Respuesta :

Katieg3593

Answer:

Step-by-step explanation:

81^x=27^(x+2)

3^4=81 and 3^3=27

3^4x=3^(3(x+2))

exponents are the same so we just take those

4x=3x+6

x=6

carlosego

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