Resposta :
a)
[tex]log_2(x-3)-log_25-1=0 \\ \\ log_2(x-3)-log_25=1 \\ \\ log_2\left(\frac{x-3}{5} \right)=1 \\ \\ \frac{x-3}{5}=2 \\ \\ x-3=10 \\ \\ \boxed{x=13}[/tex]
b)
[tex]log_2x+3log_x2=4 \\ \\ log_2x+log_x8=4 \\ \\ log_2x+\frac{log_28}{log_2x}=4 \\ \\ log_2x+\frac{3}{log_2x}=4 \\ \\ log_2x=y \\ \\ y+\frac{3}{y}=4 \\ \\ y^2+3=4y \\ \\ y^2-4y+3=0 \\ \\ y=1 \rightarrow log_2x=1 \rightarrow \boxed{x=2} \\ \\ y=3 \rightarrow log_2x=3 \rightarrow \boxed{x=8} [/tex]
[tex]log_2(x-3)-log_25-1=0 \\ \\ log_2(x-3)-log_25=1 \\ \\ log_2\left(\frac{x-3}{5} \right)=1 \\ \\ \frac{x-3}{5}=2 \\ \\ x-3=10 \\ \\ \boxed{x=13}[/tex]
b)
[tex]log_2x+3log_x2=4 \\ \\ log_2x+log_x8=4 \\ \\ log_2x+\frac{log_28}{log_2x}=4 \\ \\ log_2x+\frac{3}{log_2x}=4 \\ \\ log_2x=y \\ \\ y+\frac{3}{y}=4 \\ \\ y^2+3=4y \\ \\ y^2-4y+3=0 \\ \\ y=1 \rightarrow log_2x=1 \rightarrow \boxed{x=2} \\ \\ y=3 \rightarrow log_2x=3 \rightarrow \boxed{x=8} [/tex]