Penyelesaian dari persamaan 5^log x + x^ log 5 = 2,5 adalah.....

jawab

misalkan
⁵log x = a → ˣlog 5 = 1/a

⁵log x + ˣlog 5 = 5/2
a + 1/a  = 5/2 .....kali 2a
2a² + 2 = 5a
2a² - 5a + 2 = 0
(2a - 1)(a - 2) =0
a= 1/2  atau x = 2

⁵log x = a → x = 5ᵃ
a = 1/2  → x = 5^(1/2) = √5
a= 2 → x = 5²= 25

x = (√5, 25)

Misal :
5'log x = a

5'log x + x'log 5 = 5/2
a + 1/a = 5/2
Kedua ruas kalikan 2a
2a² + 2 = 5a
2a² - 5a + 2 = 0
(2a - 1)(a - 2) = 0

2a - 1 = 0
a = 1/2
5'log x = 1/2
x = √5 ✓

a - 2 = 0
a = 2
5'log x = 2
x = 5² = 25 ✓

NiLai x yg memenuhi :
√5 dan 25