# How do you solve ln (4x – 2) – ln 4 = - ln (x-2)?

The solution is $x = \frac{5}{2}$
$\ln \left(4 x - 2\right) - \ln 4 = - \ln \left(x - 2\right) \implies \ln \left(4 x - 2\right) + \ln \left(x - 2\right) = \ln 4 \implies \ln \left(4 x - 2\right) \left(x - 2\right) = \ln 4 \implies \left(4 x - 2\right) \left(x - 2\right) = 4 \implies 4 {x}^{2} - 8 x - 2 x + 4 = 4 \implies 4 {x}^{2} - 10 x = 0 \implies 2 x \left(2 x - 5\right) = 0 \implies x = 0 , x = \frac{5}{2}$
Because $x > 2$ the acceptable solution is $x = \frac{5}{2}$