limit of a log function?

Question

limit of: log base 5 (8x - x^4) as x approaches 2 from the left side

Answer 1

[x→2⁻]lim log₅ (8x - x⁴)

Obviously, as x→2, 8x - x⁴ → 0. Further, 8x - x⁴ is decreasing near 2, so if x approaches 2 from the left, 8x - x⁴ will approach 0 from the right. And obviously as y→0⁺, log₅ y → -∞ (this holds for a log to any base greater than 1). Therefore, we have:

[x→2⁻]lim log₅ (8x - x⁴) = [y→0⁺]lim log₅ y = -∞

Answer 2

limit of: log base 5 (8x - x^4) as x approaches 2 from the left side
approaches -infinity because 8x - x^4 approaches zero from the right side, and log base 5 (0+) ->-infinity.