Question

resolva em Ir: log (x+2)+log(3-x)=log(5x+1)

Answer 1

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

log(x+2)((3-x) = log (5x+1)
log (3x -x² + 6 - 2x) = (5x+1)

3x - x² + 6 - 2x - 5x - 1 = 0
-x² -4x + 5  = 0
Δ = (-4)² - 4(-1)(5)
Δ = 16 + 20 = 36
√Δ = 6
x1 = (4 + 6)/2(-1) = 10/-2 = -5   (não serve)
x2 = (4 - 6)/2(-1) = -2/-2 = 1

Resposta: S={x ∈ |R / x = 1}

Espero ter ajudado.

Answer 2

.
Ola Gihh

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

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

-x² + x + 6 = 5x + 1

-x² - 4x + 5 = 0

delta
d² = 16 + 20 = 36
d = 6

x = (4 - 6)/-2 = 1

pronto