Answer
No solution.
Work Step by Step
$\ln (x+4) + \ln(x+1) = 2\ln(x+3)$
$\ln (x+4)(x+1) = \ln (x+3)^{2}$
$(x+4)(x+1) = (x+3)^{2}$
$x(x+1)+4(x+1) = x(x+3)+3(x+3)$
$x^{2} + x + 4x + 1 = x^{2} + 6x + 9$
$x^{2} - x^{2} + 5x -6x + 1 - 9 = 0$
$-x - 8 = 0$
$-x = 8$
$x = -8$
No solution.