04Dloge

= 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.

Asymptote: x = 0

x-intercept: (1, 0)

2nd point: (e, 1)

Domain: x Î R +

Range: y Î R

Strictly Increasing Graph

Comparing the natural log graph to y = e x
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) → (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. Go to top of page flat .