Today in Pre-Calculus

• Go over homework• Need a calculator• Review Chapter 3• Homework

Converting to logs• Example: 16 = 4x

• Example: 17 = 3x

• Example: 183 = ex

Converting to exponents

• Example: 3 = log4x

• Example: 4 = log5x

• Example: lnx = 2

Change of Base FormulaAllows us to rewrite logs in terms of base 10 or e so we can calculate the value of the log.

log: log

logb

ab

xchange of base formula x

a

log10 : log

loga

xfor base x

a

ln: log

lna

xfor base e x

a

Example: Find the value log428

Properties of Logslog10= lne=

log10x= lnex=

log1= ln1=

10logx = elnx =

Condensing Log ExpressionsExample: condense: log5x - log5y

Example: Condense: 3lnx + 4 ln(y+4)

Expanding Log Expressions• Use the properties of logs to rewrite one log

expression into multiple log terms.

example: Expand log812y

3

6: expand ln

x yexample

z

Solving exponential Equations

2

11. 5 64

4

2. 6 10 46

3. 10 45 83

x

x

x

e

e

Solving Log EquationsExample 1: log(4x + 2) – log(x – 1) = 1

Example 2: ln(x – 2) + ln(2x – 3) = 2lnx

Interest

• Compound interest:

• Continuously Compounded interest: A=Pert

1kt

rA P

k

A: final amountP: principalr: interest ratek: number of payments per yeart: number of years

ExampleHow long will it take for an investment of $15,000 to grow to $27,000 if interest is compounded quarterly with a 7.5% interest rate?

How long will it take if the interest is compounded continuously?

Graphs

y = 2x

1

2

x

y

Transformations

y = 2x+2

Transformations

y = -2x

13

2

x

y

Additional Practice

• Pg 286: 25-30all

• Pg 308: 17-23 odd

• Pg 317: 7-11odd, 15-21odd, 23-27odd

• Pg 331: 11-15odd

• Pg 341: 21-27odd

• Pg 345: 31,32,53,54