1. 5.4: Logarithmic Functions and Models
December 8, 2008
5.4: Logarithmic Functions and Models

2. 5.4 Objectives Evaluate the common logarithmic function
Solve basic exponential and logarithmic equations
Evaluate logarithms with different bases
Solve general exponential and logarithmic equations

3. Common logarithm
log x = k if x = 10k Properties of this include: log 10x = x 10logx = x

4. Base a logarithm
logax = k if and only if.. x=ak a>0 and not equal to 1 k is a real number

5. Properties of base a logarithms
logaax=x (for any real number x)
alogax=x (for any positive number x)

6. Connecting to Inverses
The inverse function of
f(x)=ax
Is…..
loga

7. HOW TO SOLVE LOGARITHMIC EQUATIONS
In the form logax=k
Exponentiate each side with the base (a) to make the log side equal x.
Use the inverse property to find x.

8. Try these
log416 = log216 =

9. Solving exponential equations
In the form ax=k.
Take log base a on both sides, to make ax equal x.
Use the inverse property to find x.

10. Try these
4x = 1/ x = 16

11. 5.5 Objectives Apply the base properties of logarithms.
Use the change of base formula.

12. Properties of Logarithms
loga1=0 and logaa=1
logam+logan=loga(mn)
logam-logan=loga(m/n)
loga(mr)=rlogam

13. Change of base formula Let x, a, and b be positive numbers..
..where a≠ 1 and b≠ 1.

14. Try these
ln 5+ ln 4 log 10-log 5

15. And more…
log log 5 + log 15 – log 10

16. Assignment
Page 430
5, 6, 11, 12
Page
7-14
31-38