# How do you solve ln(y-1) - ln(2) = x + ln x?

Dec 12, 2015

Use property of logs ...

#### Explanation:

$\ln \left[\frac{y - 1}{2 \times x}\right] = x$

Exponentiate ...

${e}^{\ln \left[\frac{y - 1}{2 \times x}\right]} = {e}^{x}$

Simplify ...

$\frac{y - 1}{2 x} = {e}^{x}$

$y = \left(2 x\right) {e}^{x} + 1$

This function approaches $y = 1$ as $x \rightarrow - \infty$. It never crosses the x-axis.

Hope that helps