Question

Resolva a equação logx 5 + log25 x = 3/2

Answer 1

$log_x5+log_{25}x=\frac{3}{2}\\ \\ \frac{log_55}{log_5x}+\frac{log_5x}{log_525}=\frac{3}{2}\\ \\ \frac{1}{log_5x}+\frac{log_5x}{2}=\frac{3}{2}\\ \\ \boxed{y=log_5x}\\ \\ \frac{1}{y}+\frac{y}{2}=\frac{3}{2}\\ \\ \frac{2+y^2}{2y}=\frac{3}{2}\\ \\ 2y^2+4=6y\\ \\ 2y^2-6y+4=0\\ \\ S=\{1,2\}$

Logo:

$log_5x=1\Rightarrow x=5\\ \\ log_5x=2\Rightarrow x=25$