Question

Tentukan Himpunan penyelesaian dari persamaan eksponen berikut.
Menggunakan cara dan rumus logaritma ....
Bsok di kumpul kak​

Answer 1

Eksponen

(1/2)^(5 - x) = (1/6)^(2x + 1)

2^-1(5 - x) = 6^-1(2x + 1)

2^(-5 + x) = (2 × 3)^(-2x - 1)

2^(x - 5) = 2^(-2x - 1) . 3^(-2x - 1)

2^(x - 5) / 2^(-2x - 1) = 3^(-2x - 1)

2^(x - 5 - (-2x - 1)) = 3^(-2x - 1)

2^(3x - 4) = 3^(-2x - 1)

2^(3x) / 2^4 = 3^(-2x) / 3

2^(3x) / 3^(-2x) = 2^4 / 3

((2^3)/(3^-2))^x = 16/3

(8/(1/9))^x = 16/3

(8 × 9)^x = 16/3

x log 72 = log (16/3)

x = log (16/3) / log 72

x = ⁷²log (16/3)

x = ⁷²log 16 - ⁷²log 3

Cara lain :

log 2^(-5 + x) = log 6^(-2x - -1)

(-5 + x) log 2 = (-2x - 1) log 6

(x - 5) log 2 = (-2x - 1)(log 2 + log 3)

(x - 5) log 2 - (-2x - 1) log 2 = (-2x - 1) log 3

(x - 5 + 2x + 1) log 2 = (-2x - 1) log 3

(3x - 4) log 2 = (-2x - 1) log 3

3x log 2 - 4 log 2 = - 2x log 3 - log 3

3x log 2 + 2x log 3 = 4 log 2 - log 3

x (3 log 2 + 2 log 3) = 4 log 2 - log 3

x log (2³ × 3²) = log (2⁴/3)

x = log (16/3) / log 72

x = ⁷²log (16/3)

HP = {⁷²log (16/3)}