## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$x=\dfrac{1}{e^2-1} \approx 0.157$
Apply the logarithmic property: $\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$ and rearrange the given expression to obtain: $\ln \left(\dfrac{x+1}{x} \right) = 2$ or, $e^2 =\dfrac{x+1}{x}$ or, $e^2 \ x=x+1$ or, $x(e^2-1)=1$ or, $x=\dfrac{1}{e^2-1}$ Thus, our answer is: $x=\dfrac{1}{e^2-1} \approx 0.157$