Answer
$x=1$
Work Step by Step
$3\log_2 2x+\log_2 16=7$
$3\log_2 2x+\log_2 2^4=7$
$3\log_2 2x+4=7$
$3\log_2 2x=7-4$
$3\log_2 2x=3$
$\log_2 2x=\frac{3}{3}$
$\log_2 2x=1$
In exponential form
$2^1=2x$
$2x=2$
$x=1$
Note; Check the solution in the given equation.