Answer: No real solution
Step-by-step explanation:
log₂(9x² + 30x + 25) = 8
we know that ㏒ₐx = b ⇔ aᵇ = x with a>0 and ≠1 and x >0. This way,
9x² + 30x + 25 = 2⁸
9x² + 30x + 25 = 256
9x² + 30x + 25 - 256 = 0
9x² + 30x - 231 = 0
Δ = 30²-4.9.231 = -7416
No real solution.
Log existence condition:
9x² + 30x + 25 > 0
Δ = 30²-4.9.25 = 0
x = -30/18 = -5/3 = -1.667
x ≠ -5/3
