Logarithmic Functions
The logarithmic function f with base b, defined by
is the inverse of the exponential function with base b.
Properties of
The y-axis is the vertical asymptote of the graph.
The x-intercept of the graph is 1.
The graph is increasing when b > 1, while the graph is decreasing if 0 < b < 1.
The function is one-to-one.
Solving Logarithms
Given the expression logbx, we are looking for the
exponent of b that will give x.
How to sketch the graph?
1. Find the vertical asymptote. How?
2. Determine two arbitrary points. What points?
Use and
3. Locate the points.
4. Use the asymptote-two-point technique!
1hxc bhxc
x h
The natural expo and log functions
The natural exponential function is defined by
The natural logarithmic function is defined by
.xf x e
ln .f x x