x^log (x^2-3x-4) < x^log (x+1)
Matematika
nanun1
Pertanyaan
x^log (x^2-3x-4) < x^log (x+1)
2 Jawaban
-
1. Jawaban devidmanurung
x^log (x^2-3x-4) < x^log (x+1)
log (x^2-3x-4) < log (x+1)
log (x-4)(x+1) < log (x+1)
log (x-4) + log (x+1) < log (x+1)
log (x-4) < log (x+1) - log (x+1)
log (x-4) < 1
log (x-4) < log10
x-4 < 10
X < 14 -
2. Jawaban arsetpopeye
xlog(x^2 - 3x - 4) < xlog(x + 1)
(x^2 - 3x - 4) < (x + 1)
x^2 - 4x - 5 < 0
(x - 5)(x + 1) < 0
x = 5 atau x = -1
++++ (-1) ---- (5) ++++ ==> arsir daerah yang negatif
SYARAT
1) x^2 - 3x - 4 > 0
(x - 4)(x + 1) >
x = 4 atau x = -1
+++ (-1) ----- (4) ++++ ==> arsir daerah yang positif
2) x + 1 > 0 => x > -1
3) x > 0
4) x ≠ 1
Irisan garis bilangan penyelesaian dengan syarat
............. (-1) xxxxxxxxxxxxxxxxx (5) .............
1) xxxx (-1) .................... (4) xxxxxxxxxxxxxx
2) ......... (-1) xxxxxxxxxxxxxxxxxxxxxxxxxx
3) .................. (0) xxxxxxxxxxxxxxxxxxxxxx
HP = {x | 4 < x < 5, x € R}