Question

ME AJUDE A RESOLVER : LOGARITMO
LOG3(X²-5X+13)= 3

Answer 1

Vejamos:

log3^(x²-5x+13) = 3
log3³ = x² - 5x + 13

x² - 5x + 13 = 27
x² - 5x + 13 - 27 = 0
x² - 5x - 14 = 0

Δ = 25 + 56 = 81 
√81 = 9

x' = (5 + 9)/2 = 7
x'' = (5-9)/2 = - 2
ou x = 7 ou x = -2

Answer 2

$log_{3} (x^{2}-5x+13)=3 \\ \\ x^{2} - 5x + 13 = 3^{3} \\ \\ x^{2}-5x + 13 = 27 \\ \\ x^{2} - 5x + 13 - 27 = 0 \\ \\ x^{2}-5x - 14=0 \\ \\ D = (-5)^{2}-4(1)(-14) \\ \\ D= 25 + 56 = 81 \\ \\ \sqrt{D} = 9 \\ \\ x' = \frac{ (5 + 9)}{2} = \frac{14}{2} = 7 \\ \\ x'' = \frac{ (5 - 9)}{2} = \frac{-4}{2} = -2 \\ \\ V=\{-2;7\}$

Espero ter ajudado.