COLLEGEALGEBRA
Lesson: Logarithmic Function
Objectives: 1. To graph a logarithmic function;
2. To solve basic logarithmic equations.
Because the exponential function is one-to-one, then
↔
.
The expression is called “the logarithm in base a of y”.
If a > 0 with 1, then the logarithmic function with the base a is:
:0,∞→,
.
Graphs of logarithmic functions:
a. If a > 1 b. If 0 < a < 1
Properties of the graphs:
1. If a > 1, the logarithmic functions are increasing; if a < 1 they decrease;
2. The logarithmic function
crosses the x-axis in the point (1,0) for any
positive value of a;
3. The logarithmic function
does not touch the y-axis; the y-axis is a vertical
asymptote for the function;
4. The logarithmic function is one-to-one:
→ .
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