1. 3.3 Logarithmic Functions and Their Graphs

2. Logarithmic Functions
The inverse of
y = bx is
y = logbx

3. Logarithmic Basic Properties
logb 1 = 0 because b0 = 1
ex) log9 1 =
logb b = 1 because b1 = b
ex) log3 3 =
logbby = y because by = by
ex) log4 42 =
blogbx = x because logb x = logb x
ex) 7log73 =

4. You Try! Evaluate Each Expression
log232
Log9√9
log644
5log517
log6(1/216)

5. Common Logarithms (Logs with base 10)
log 1 = 0 because 100 = 1
log 10 = 1 because 101 = 10
Log 10y = y because 10y = 10y
ex) log =
1000
10log x = x because log x = log x
ex) 10log(.5) =

6. Evaluate using calculator & Check
log 9.43 ≈
Check:
log (-14) =
You Try!
log 34.5 ≈
Check:

7. Solving Logarithmic Equations
log x = 2
Log5 x = -3
You Try!
log x = -1
Log4 x = 6

8. Natural Logarithms : Base e
logex = ln x
y = ln(x) is the inverse
of the exponential function y = ex

9. Natural logarithms ln 1 = 0 because e0 = 1 ln e = 1 because e1 = e
ln ey = y because ey = ey
ex) ln e3 =
elnx = x because ln x = ln x
ex) eln 6 =

10. You Try! Evaluate:
ln e -4
ln 1/e
ln 4√e
ln 4.05 ≈
Check:

11. g(x) = ln (x + 2)
h(x) = ln (3 – x)
g(x) = 3 log x
h(x) = 1 + log x

12. Homework
Pg : 4, 10, 14, 22, 24, 26, 32, 36, 44, 58