# How do you solve Ln (y) – Ln (y-4) = Ln (2) ?

Mar 10, 2016

$y = 8$

#### Explanation:

putting everything on one side we get

$\ln y - \ln \left(y - 4\right) - \ln 2 = 0$

Use the property that ${\log}_{b} \left(\frac{x}{y}\right) = {\log}_{b} x - {\log}_{b} y$

$\ln \left(\frac{y}{2 \left(y - 4\right)}\right) = 0$

Take the inverse log, in this case the inverse of $\ln \left(x\right)$ is ${e}^{x}$

${e}^{0} = \frac{y}{2 \left(y - 4\right)}$

$1 = \frac{y}{2 \left(y - 4\right)}$

$2 y - 8 = y$

$2 y - y = 8$

$y = 8$