04 61loggraphse

# Logarithm Graphs (Base e)

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

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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: $x \in R^+$
• Range: $y \in R$
• Strictly Increasing Graph

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## Comparing the natural log graph to y = ex

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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.
• $(x, \; y) \rightarrow (y, \; x)$

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## 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.

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