today in pre-calculus go over homework need a calculator review chapter 3 homework
TRANSCRIPT
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
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 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?