1. Logarithmic Functions & Their Graphs
Sec. 5.2
Logarithmic Functions & Their Graphs

2. Logarithmic Function is the inverse of exponential function
Definition of Logarithmic Function
y = logax if and only if x = ay
f(x) = logax for x>0 & a>0, a≠1
Natural log is represented by ln
y = ln x means logex if x = ey

3. logax Means what exponent must a be raised to to get x. log28
Means what must 2 be raised to in order to get 8.
log28 = 3

4. log93 Set it up in exponential form 9x = 3 Try these log66 log5(1/25)

5. Common Logarithmic Function
Has 10 as its base
Denoted with just log
What the log on the calculator represents

6. What would these be?
log 10
2 log 2.5
log (-2)

7. Properties of Logarithms
logaa=1
logaax=x
If logax = logay then x=y

8. also
ln 1 = 0
ln e = 1
ln ex = x
If ln x = ln y then x=y