Question

1) log (x-3) na base 2 - log 5 na base 2 -1 = 0

2) log x na base 2 + 3 log 2 na base x = 4

Answer 1

a)
$log_2(x-3)-log_25-1=0 \\ \\ log_2(x-3)-log_25=1 \\ \\ log_2\left(\frac{x-3}{5} \right)=1 \\ \\ \frac{x-3}{5}=2 \\ \\ x-3=10 \\ \\ \boxed{x=13}$

b)
$log_2x+3log_x2=4 \\ \\ log_2x+log_x8=4 \\ \\ log_2x+\frac{log_28}{log_2x}=4 \\ \\ log_2x+\frac{3}{log_2x}=4 \\ \\ log_2x=y \\ \\ y+\frac{3}{y}=4 \\ \\ y^2+3=4y \\ \\ y^2-4y+3=0 \\ \\  y=1 \rightarrow log_2x=1 \rightarrow \boxed{x=2} \\ \\ y=3 \rightarrow log_2x=3 \rightarrow \boxed{x=8}$