Question

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

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

Answer 1

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

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