Question

Tentukan HP dari

3 Log^2(x+1) - 4.3log(x+1) + 3 log 27 = 0

Answer 1

³log²(x+1) - 4.³log(x+1) + ³log27 = 0
³log²(x+1) - 4.³log(x+1) + ³log3³ = 0
³log²(x+1) - 4.³log(x+1) + 3.³log3 = 0
³log²(x+1) - 4.³log(x+1) + 3 = 0

Misal
³log(x + 1) = a

a² - 4a + 3 = 0
(a - 3)(a - 1) = 0

a - 3 = 0
a = 3
dan
a - 1 = 0
a = 1

Untuk a = 3
³log(x + 1) = 3
x + 1 = 3³
x + 1 = 27
x = 27 - 1
x = 26

Untuk a = 1
³log(x + 1) = 1
x + 1 = 3¹
x + 1 = 3
x = 3 - 1
x = 2

HP = {2, 26}