Question

Dengan cara
Silahkan jawab

Answer 1

1.
²log (x + 5) + ²log (3 - x) < ²log (4 - x)
²log ((x + 5)(3 - x)) < ²log (4 - x)
²log (-x² - 2x + 15) < ²log (4 - x)
syarat 1 :
-x² - 2x + 15 < 4 - x
-x² - 2x + x + 15 - 4 < 0
-x² - x + 11 < 0
x² + x - 11 > 0
x² + x - 11 = 0
(x + 1/2)² - 1/4 - 11 = 0
(x + 1/2)² - 45/4 = 0
(x + 1/2)² = 45/4
x + 1/2 = √(45/4)
x + 1/2 = (3/2)√5 atau x + 1/2 = - (3/2)√5
x = (3/2)√5 - 1/2 atau x = -(3/2)√5 - 1/2
x = (3√5 - 1)/2 atau x = (-3√5 - 1)/2
+++ ---- ++++
______________________
(-3√5 - 1)/2 (3√5 - 1)/2
x < (-3√5 - 1)/2 atau x > (3√5 - 1)/2 ... (1)

syarat 2 :
setelah log nilai harus positif
-x² - 2x + 15 > 0
x² + 2x - 15 < 0
x² + 2x - 15 = 0
(x + 5)(x - 3) = 0
x = -5 atau x = 3
+++ ---- +++
_______________
-5 3
-5 < x < 3 ... (2)

4 - x > 0
-x > -4
x < 4 ... (3)

iris persamaan (1), (2) dan (3)
Hp = {x| -5 < x < (-3√5 - 1)/2 atau (3√5 - 1)/2 < x < 3}

2.
²log (x² -3x + 2) < ²log (10 - x)
syarat 1 :
x² -3x + 2 < 10 - x
x² - 3x + x + 2 - 10 < 0
x² - 2x - 8 < 0
x² - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 atau x = -2
+++ ---- ++++
____________
-2 4
-2 < x < 4 ... (1)
syarat 2 :
setelah tulisan log nilainya harus positif
x² -3x + 2 > 0
x² -3x + 2 = 0
(x - 2)(x - 1) = 0
x = 2 atau x = 1
+++ ---- ++++
_____________
1 2
x < 1 atau x > 2 ... (2)
10 - x > 0
-x > -10
x < 10 ... (3)
iris persamaan (1), (2) dan (3)
Hp = {x| -2 < x < 1 atau 2 < x < 4}

3.
^12log 75
= (³log 75)/(³log 12)
= (³log (3.5²))/(³log(4.3))
= (³log 3 + ³log 5²)/(³log 4 + ³log 3)
= (³log 3 + 2.³log 5)/(³log 4 + ³log 3)
= (1 + 2.(1/a))/(b + 1)
= (1 + 2/a)/(b + 1)
= (a + 2)/(a(b + 1))
= (a + 2)/(ab + a)

diketahuinya sedikit dimanipulasi ya
³log 4 = b
³log 2² = b
2.³log 2 = b
³log 2 = b/2

^60log 120
= (³log 120)/(³log 60)
= (³log (2³.3.5)/(³log (2².3.5))
= (³log 2³ + ³log 3 + ³log 5)/(³log 2² + ³log 3 + ³log 5)
= (3.³log 2 + ³log 3 + ³log 5)/(2.³log 2 + ³log 3 + ³log 5)
= (3.(b/2) + 1 + 1/a)/(2.(b/2) + 1 + 1/a)
= ((3b)/2 + 1 + 1/a)/(b + 1 + 1/a)
= (3ab + 2a + 2)/(2a))/(ab + a + 1)/a)
= (3ab + 2a + 2)/(2.(ab + a + 1))
= (3ab + 2a + 2)/(2ab + 2a + 2)