Answer
$x = \frac{2}{9}$
$x = 0.22$
Work Step by Step
$\log (x+4) - \log 2 = \log (5x+1)$
$\log \frac{x+4}{2} = \log (5x+1)$
$\log \frac{x+4}{2} - \log (5x+1) = 0$
$\log \frac{x+4}{2(5x+1)} = 0$
$1 = \frac{x+4}{2(5x+1)}$
$\frac{x+4}{2(5x+1)} = 1$
$\frac{x+4}{10x+2} = 1$
$x+4 = 1(10x+2)$
$x+4 = 10x + 2$
$x - 10x = -4 + 2$
$-9x = -2$
$x = \frac{2}{9}$
by GDC / calculator
$x = 0.22$