# How do you solve log(x+3)+log(x)=1?

${\log}_{10} \left(x + 3\right) + {\log}_{10} \left(x\right) = 1 \to {\log}_{10} \left(\left(x + 3\right) \left(x\right)\right) = 1 \to {\log}_{10} {x}^{2} + 3 x = 1 \to {10}^{1} = {x}^{2} + 3 x$
$0 = {x}^{2} + 3 x - 10 \to 0 = \left(x + 5\right) \left(x - 2\right) \to x = - 5 , x = 2$