Soal dan Pembahasan Logaritma Kelas X Sukino Peminatan LKS 5 Bag C no 4

 4. Carilah nilai x (dengan asumsi a > b > 0) yang memenuhi persamaan :

(a⁴ - 2a²b² + b⁴)^{x - 1} = (a - b)^2x(a + b)

Jawaban :

(a⁴ - 2a²b² + b⁴)^{x - 1} = (a - b)^2x(a + b)

berikan log di kedua sisi :

log (a⁴ - 2a²b² + b⁴)^{x - 1} = log ((a - b)^2x(a + b))

(x - 1) log (a⁴ - 2a²b² + b⁴) = log (a - b)^2x + log(a + b)

(x - 1) log (a² - b²)² = 2x log (a - b) + log(a + b)

2 (x - 1) log (a² - b²) = 2x log (a - b) + log(a + b)

2 (x - 1) log (a - b)(a+b) = 2x log (a - b) + log(a + b)

(2x - 2) (log (a - b) + log (a + b)) = 2x log (a - b) + log(a + b)

2x log (a - b) + 2x log (a + b) - 2 log (a - b) - 2 log (a + b) = 2x log (a - b) + log (a + b)

2x log (a - b) + 2x log (a + b) - 2 log (a - b) - 2 log (a + b) = 2x log (a - b) + log (a + b)

2x log (a + b) - 2 log (a - b) - 3 log (a + b) = 0

(2x - 3) log (a + b) = 2 log (a - b)

2x - 3 = 2 log (a - b) / log (a + b)

2x = (2 log (a - b) / log (a + b)) + 3

x = ((2 log (a - b) / log (a + b)) + 3) / 2