Final answer:
To solve the equation 2^(x+2) = 8^(-x+8), the base 8 is expressed as 2^3, resulting in an equation with a common base. The exponents are then equated and solved for x, yielding the solution x = 5.5.
The correct answer is c. 5.5.
Step-by-step explanation:
To solve the exponential equation 2x+2 = 8-x+8, we must recognize that 8 is a power of 2, since 8 = 23. Therefore, we can rewrite the equation with a common base:
2x+2 = (23)-x+8
Now apply the power rule (am)n = amn, which gives:
2x+2 = 2-3x+24
Since the bases are the same, we can equate the exponents:
x + 2 = -3x + 24
Now, solve for x:
4x = 22
x = 22 / 4
x = 5.5
Therefore, the correct answer is c. 5.5.