Question

2log₅^2 *x+5log₅ x+2=0

Answer 1

$2log_5^2x+5log_5x+2=0|x\ \textgreater \ 0\\t=log_5x\\\\2t^2+5t+2=0\\D=5^2-4*2*2=25-16=9=3^2\\t_1= \frac{-5+3}{2*2}= \frac{-2}{4}=- \frac{1}{2}\\t_2=\frac{-5-3}{2*2}= \frac{-8}{4}=-2\\\\log_5x=- \frac{1}{2}\\x=5^{- \frac{1}{2}}\\x_1= \frac{1}{ \sqrt{5} }= \frac{ \sqrt{5} }{5} }\\\\log_5x=-2\\x=5^{-2}\\x_2= \frac{1}{25}$