7. Principal nth root
Where n=positive integer greater than 1
= real number
Value for Value for
= positive real number b
Such that
=negative real number b
Such that
8. Properties of
RADICAL
index
radicand
Radical sign
PROPERTY EXAMPLE
13. How do you know when a
radical problem is done?
(1) No radicals can be simplified.
Example:
8
(2) There are no fractions in the radical.
Example: 1
4
(3) There are no radicals in the denominator.
Example: 1
5
17. How do you simplify variables in the radical?
7
x
Look at these examples and try to find the pattern…
1
x x What is the answer to x7 ?
2
x x x 7
x 3
x
3
x x x
4 2
As a general rule, divide the
x x exponent by two. The
x 5 2
x x remainder stays in the
6 3 radical.
x x
21. • The logarithmic function with base is one-to-
one. Thus, the following equivalent conditions
are satisfied for positive real number x1 and x2 .
(1) If x1 x2 , then .
(2) If , then x1 x2 .
22. Example :
Solving a logarithms equation.
Check..
Since is a true statement, then
23. • Definition of common logarithm:
for every
• Defition of natural logarithm:
for every
25. = Power to which you need to raise 2 in order to get 8
(a) log28
= 3 ( Since 23 = 8 )
= Power to which you need to raise 4 in order to get 1
(b) log41
= 0 ( Since 40 = 1 )
= Power to which you need to raise 10 in order to get 10,000
(c) log1010,000
= 4 ( Since 104 = 10,000 )
= Power to which you need to raise 10 in order to get 1/100
(d) log101/100
= 2 ( Since 10-2 = 1/100 )