Question

Dada a equação logx (5x−6) = 2. Calcule seu conjunto solução.

Answer 1

$\mathrm{\log_x{(5x-6)}=2\ \to\ x^2=5x-6\ \to\ x^2-5x+6=0}\\\\ \mathrm{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-5)\pm\sqrt{(-5)^2-4.1.6}}{2.1}=}\\\\ \mathrm{=\dfrac{5\pm\sqrt{25-24}}{2}=\dfrac{5\pm\sqrt{1}}{2}=\dfrac{5\pm1}{2}=\boxed{\mathrm{3}}\ ou\ \boxed{\mathrm{2}}}\\\\ \boxed{\boxed{\mathbf{x=\{2,3\}}}}$