Question

Como resolver:
2(log de x na base 5)^2+log de x na base 5=1

Answer 1

$2(log_5x)^2+log_5x=1\\ \\ \boxed{y=log_5x}\\ \\ 2y^2+y-1=0\\ \\ \Delta=1^2-4.2.(-1)=1+8=9\\ \\ y=\frac{-1\pm3}{4}\\ \\ y_1=-1\\ \\ y_2=\frac{1}{2}$
$Logo: log_5x=\frac{1}{2}\Rightarrow x=5^{\frac{1}{2}}=\sqrt5\\ \\ ou\\ \\ log_5x=-1\Rightarrow x=5^{-1}=\frac{1}{5}$