EXPONENTS AND LOGARITHMIC FUNCTIONS
Exponents ­
6
3
6
­3 = 6 ∙ 6 ∙ 6
= 1/6 3 = 1/(6∙ 6∙ 6)
4 √625 = 4
1/2
8
1/3 x
1/n
125
(36)
5
√16807 = when exponent is fraction = 3 √8 = 2 What number √4 = 2
∙ What number ∙What number = 8
= n √x 2/3
5/2
= [(125)
= [√32]
1/3 2
] = ( 3 √125) 2 = 5 2 = 25
5
= 6 5 = 7776
1
Exponential Growth and Decay
x
y = ab
a = original amount
b = growth or decay rate
x = time periods
Exponential Growth or Decay?
Graph y = 4(2)
x
x y
2
Logarithmic Functions ­ another way to write exponents
Base
exponent
= Answer 2
Using logs ­ log
base
log log 5
= 32
answer = exponent 2 32 = 5
3 729 = 6 3
6
= 729
Write in exponential form
log 2 16 = 4 log 5 625 = 4
Write in logarithmic form
7
3
4
­2
8
1/3
10
= 343 = 1/16
3
= 2
= 1000
3
Find the value of n.
log 2 n = 4
n = log log 5 125
n 100,000 = 5
log 5 1/5 = n
log 6 √6 = n
log 81 n = 5/4
log x 8 = 3/4
log 10 1,000,000 = n
4
Common Logarithms are logarithms with base 10
y = log 10 x or y = log x (If there is no base number, use 10)
Finding common logs of powers of 10 easy to find without calculator.
x
log 100 = 10
= 100
x = log 1,000,000 = log .1 = log 1000 = log 10
8
= What if you aren't using powers of 10? CALCULATOR!!!!
log 5 = log 12 = log x = 1.5 know this is base 10
10
1.5 = x
Writing the problems WILL help!!!!
5
Logarithmic Functions are inverses of exponential functions (exp growth/decay)
Graph y = 2
x
exponential growth.
x y
x
The inverse of y = 2
is
log 2 x = y
Don't worry how ­ later mathematics
Worry about what a log function
will look like!!!
6