Question

Solve 81^x = 27^^^x + 2.

A. x = 1
B. x = 2
C. x = 5
D. x = 6

Answer 1

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

Answer 2

For this case we must solve the following equation:

`81 ^ x = 27^(x + 2)`

We rewrite:

`81 = 3 ^ 4\\27 = 3 ^ 3`

Then, replacing:

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

For the bases to be equal then it must be fulfilled that:

`4x = 3 (x + 2)\\4x = 3x + 6\\4x-3x = 6\\x = 6`

Answer:

`x = 6`

Option D