×

# How to find the value of a?

Mar 8, 2018

$a = e$

#### Explanation:

Given the line

$y = m x$

and the curve

$y = \ln x$

The tangency conditions are

$\left\{\begin{matrix}y = \ln x \\ y = m x \\ y ' = \frac{1}{x} \\ y ' = m\end{matrix}\right.$

hence

$\left\{\begin{matrix}\ln x = 1 \\ x = e\end{matrix}\right.$

determines the tangency point and consequently

$y = \frac{x}{e}$ is the tangent line to $y = \ln x$ at point $x = e$