Question

log(x-2)na base 2+logX na base 2=3

Answer 1

$log_2~(x-2)+log_2~x = 3\\ \\ Pela\ propriedade:\\ \\ \large\boxed{log_b~a+log_b~c = log_b~~(a\cdot~c)}\\ \\ Ent\~ao,\ temos\ que:\\ \\ log_2~(x-2)\cdot~x = 3\\ \\ 2^3 = x(x-2)\\ \\ 8 = x^2-2x\\ \\ x^2-2x-8=0\\ \\ \Delta=b^2-4ac\\ \Delta=2^2-4(1)(-8)\\ \Delta=4+32\\ \Delta=36\\ \\ \large\boxed{x=\frac{-b+\ ou\ -\sqrt{\Delta}}{2a}}\\ \\ x' = \frac{2+6}{2} = \frac{8}{2} = 4\\ \\ x'' = \frac{2-6}{2} = \frac{-4}{2} = -2\\ \\ Como\ negativo\ n\~ao\ entra\ no\ resultado\ final,\ ficamos\ com:\\ \\ \boxed{x=4}$