# How do you solve Ln(5x-4)=ln2+ln(x+1)?

$x = 2$
Taking $\ln \left(5 x - 4\right) = \ln \left(2\right) + \ln \left(x + 1\right)$ or equivalently $\ln \left(5 x - 4\right) - \ln \left(2 \cdot \left(x + 1\right)\right) = 0$ or $\ln \left[\frac{5 x - 4}{2 \left(x + 1\right)}\right] = \ln \left(1\right)$ then results in
$\frac{5 x - 4}{2 \left(x + 1\right)} = 1$ or $5 x - 4 = 2 \left(x + 1\right)$ and finally $x = 2$