#### Answer

$\dfrac{16}{5}$

#### Work Step by Step

The domain of the variable requires that $5x>0$
$\therefore x>0$
Recall:
$y = \log_a b \text{ is equivalent to } b=a^y$
Thus,
$\log_2 (5x) = 4 \text{ is equivalent to } 5x = 2^4$
Solve the equation to obtain:
$5x = 2^4$
$5x = 16$
$x=\boxed{\frac{16}{5}}$