Matematika

Pertanyaan

Mohon bantuannya yah ka
Nomor 5 aja
Mohon bantuannya yah ka Nomor 5 aja

1 Jawaban

  • jawab
    persamaan logaritma
    ⁴log x = 1/2. ²log x
    ²log √x = 1/2. ²log x

    misal ⁴log x = ²log √x = a
    1/2. ²log x = a --> ²log x = 2a 
    x= (2)²ᵃ

    (⁴log x)²- ²log √x  -  3/4 = 0
    a² - a  - 3/4 = 0 ....kalikan 4
    4a² - 4a - 3 = 0
    (2a - 3)(2a + 1) = 0
    a = 3/2  atau a  = - 1/2

    (i) x = (2)²ᵃ
    a = 3/2 --> x = (2)²⁽³/²) = 2³ = 8
    a = -1/2 --> x = (2)²⁽⁻¹/²) = 2⁻¹ = 1/2

    (ii) syarat pembatas x> 0 

    HP (i) n (ii)  x = 8 atau x = 1/2
    x1 + x2 =  8 + 1/2 =  8¹/₂