Easy Algebra

Easy Algebra #mastertmathsclass #math #mathcompetition #shorts

[@alvinchow-beta8374]

25ˣ + 5ˣ = 20
(5²)ˣ + 5ˣ = 20
(5ˣ)² + 5ˣ = 20
Let u = 5ˣ
u² + u = 20
u² + u - 20 = 0
(u + 5)(u - 4) = 0
u = -5 or u = 4
∴5ˣ = -5 (rejected) or 5ˣ = 4
log₅(5ˣ) = log₅(4)
x = log(4) / log(5)
x = log(2²) / log(5)
x = 2log(2) / log(5)

[@user-xh3ih4ks9y]

令5^x=a 則a^2+a=20. 則a=4
則x=log4/log5

[@MasterTMathsClass]

@@user-xh3ih4ks9y 🎉

[@alvinchow-beta8374]

Here is my full solution:
25ˣ + 5ˣ = 20
(5²)ˣ + 5ˣ = 20
(5ˣ)² + 5ˣ = 20
Let u = 5ˣ
u² + u = 20
u² + u - 20 = 0
(u + 5)(u - 4) = 0
u = -5 or u = 4
∴5ˣ = -5 (rejected) or 5ˣ = 4
log₅(5ˣ) = log₅(4)
x = log(4) / log(5)
x = log(2²) / log(5)
x = 2log(2) / log(5)