3.3a.notebook
December 12, 2011
Logarithmic Functions
Def: The log of x with base b (b>0,b≠1), denoted logbx, is defined as follows:
1. Write an exponential model if a substance
has a half­life of 8 days and it initially had 10 pounds.
y = logbx iff by = x
ex. log232 = 5 then 52 = 32
Relationship between exponential functions
and log functions.
Rewrite in exponential form and Evaluate:
Graph y = 2x and y = log2x. How are they related to each other?
1. log381= Ask 3 raise to what power = 81?
2. log51= Does it matter what b is on this one?
3. log55 =
4. log497=
In general: y = bx and y = logbx are
inverses of each other.
Basic Properties:
log
log
log
b
5. log2(1/8)=
1
3.3a.notebook
December 12, 2011
Types of Logs
1. Common Log....base 10
Types of Logs
y = log10x or y = log x
2. Natural Log....base e
On calculator: log 100 = y = logex or y = ln x
y
Properties: log 1 = 0
log 10 = 1
log10 = y
10 logx = x
ex. Evaluate: log
10log5
log
Properties: ln 1 = 0 lney = y
ln e = 1 e lnx = x
ex. Evaluate: ln
eln5
lne4
Use calculator ln 12
Practice:
1. Evaluate: log 1,000,000
Journal: Explain how to evaluate
log525 in words. What are you finding?
2. Evaluate: ln e2
3. Evaluate: eln3
4. Solve for x by changing to exponential form.
log x = 2.5
2