Answer
$x = 5$
Work Step by Step
$\log (5x+1) = \log (2x+3) + \log 2$
$\log (5x+1) = \log [2(2x+3)]$
$\log(5x+1) - \log[2(2x+3)] = 0$
$\log (5x + 1) - \log (4x + 6) = 0$
$\log \frac{5x+1}{4x+6} = 0$
$1 = \frac{5x+1}{4x+6}$
$\frac{5x+1}{4x+6} = 1$
$5x + 1 = 1(4x+6)$
$5x + 1 = 4x + 6$
$5x - 4x + 1 - 6 = 0$
$x - 5 = 0$
$x = 5$
