3.2 Notes
Precalculus Sec 3.2 Logarithmic Functions
­ a logarithmic function is the inverse of an exponential function
DEF.
For x>0, a>0, and a≠1
if and only if
For example, reads "log base a of x"
1
3.2 Notes
Examples
2
3.2 Notes
­ The base of a logarithm can be any positive number except 0 and 1,
there are two that are used the most, base 10 and base e.
we don't need to write the base 10, it is implied
a log base e is called the natural logarithm and written as
Properties of logarithms with any allowed base
1) 2)
3)
4) If then
End Day 1
3
3.2 Notes
Sec. 3.2 Day 2
The graph of comes from the fact that logarithms are inverses with Domain: x>0
Range: all real
x­intercept: x=1
increasing throughout domain
V.A.: x=0 4
3.2 Notes
Transformations ­ same rules as before for shifts, reflections
EXAMPLE
Parent: is the parent function after being...
­ When graphing the logarithm function, concentrate on the vertical asymptote for the shifts left and right, and the x­intercept for the shifts up and down.
Sketch g(x) from above.
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3.2 Notes
Finding Domain of logarithmic functions You can not take the log of a negative number or of zero.
EXAMPLE
Find the domain, x intercept and the vertical asymptote of 6