Answer to Question #223085 in Algebra for Darren Agbor

Question

Log₂X + Log_x2 = 2, find x

Answer 1

$\log_2x + log_x 2 =2 \\= log_2x + \frac{1}{\log_2x}= 2 \\\text{Let $\log_2x=y$} \\y + \frac{1}{y}=2 \\=y^2 +1=2y \\=y^2 -2y+1=0 \\(y-1)^2=0 \\y=1 \\\text{Recall that $log_2x=1$} \\\implies x =2$