急急急！！！！！！！！！log的问题

itachiX

各位大大，请帮我.
2log(x+1)-log(x+2)=log(2x-1)
答案是1.3028
怎么做啊

中女_D

2log(x + 1) - log(x + 2) = log(2x - 1)
• for x > 1/2 ← log(m) only real for m > 0
log((x + 1)² ) - log(x + 2) = log(2x - 1) ← power rule
log((x + 1)² / (x + 2)) = log(2x - 1) ← quotient rule
(x + 1)² / (x + 2) = 2x - 1
(x + 1)² = (2x - 1)(x + 2)
x² + 2x + 1 = 2x² + 3x - 2
3 = x² + x
3 + 1/4 = x² + x + (1/2)² ← completing the square (or use quadratic formula)
13/4 = (x + 1/2)²
±√(13) / 2 = x + 1/2
x = -1+√(13) / 2 and reject solution out of domain
so
x ≈ 1.3028

加油~