Intersection of a logarithm and a line

Find where the logarithm $y = \ln x$ meets the line $y = 1$. At the crossing the $y$ values are equal, so $\ln x = 1$; exponentiating both sides gives $x = e^1 = e$.

The intersection is therefore $(e, 1)$, with $e \approx 2.718$, shown by the large dot. Since $y = \ln x$ is defined only for $x > 0$ and increases slowly, it meets the horizontal line $y = 1$ at exactly one point.