04 61loggraphse

Logarithm Graphs (Base e)

.

Recall that $\log_e(x)$ is often written as ln(x) {Natural Logarithm}

.

The graph of y = ln(x) follows the same rule as all other log graphs.

04.61ln1.gif
  • Asymptote: $x = 0$
  • x-intercept: $(1, \; 0)$
  • 2nd point: $(e, \; 1)$
  • Domain: $x \in R^+$
  • Range: $y \in R$
  • Strictly Increasing Graph

.

Comparing the natural log graph to y = ex

.

Recall that a log graph is the inverse of the exponential graph with the same base.

Therefore the natural log graph $y = \log_e(x)$ is the inverse of the $y = e^x$ graph.

  • This means that it is a reflection across the line $y = x$
  • or that the x and y coordinates of each individual point are swapped.
    • $(x, \; y) \rightarrow (y, \; x)$

.

Transformations on the Standard Natural Log Graph

We can apply the usual transformations such as dilations, translations and reflections when sketching the natural log graph.

.

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License