penyelesaian persamaan 9log x- xlog3=1/2

Bab Logaritma
Matematika SMA Kelas X 

^ = pangkat

⁹log x - ˣlog 3 = 1/2
1/(ˣlog 9) - ˣlog 3 = 1/2
1/(ˣlog 3²) - ˣlog 3 = 1/2
1/(2 . ˣlog 3) - ˣlog 3 = 1/2

ˣlog 3 = p

1/(2p) - p = 1/2

**semua dikalikan 2p**

1 - 2p² = p
2p² + p - 1 = 0
(2p - 1) (p + 1) = 0
2p - 1 = 0
2p = 1
p = 1/2

p + 1 = 0
p = -1

ˣlog 3 = 1/2
x^(1/2) = 3
(x^(1/2))² = 3²
x = 9

ˣlog 3 = -1
x⁻¹ = 3
x⁻¹ = (1/3)⁻¹
x = 1/3

jadi, x = 1/3 atau x = 9