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Unformatted text preview: Exponential and
Logarithmic Functions
Logarithmic
Section 5.1 nth Roots
nth
Let c be a real number and n a positive integer:
The nth root of c is denoted by either of the
nth
symbols
symbols
n c or c 1
n and is defined to be
solution of x = c when n is odd; or
n The nonnegative solution of
The
x = c when n is
even and c > 0. The
The n Defn. of Rational Exponents
Defn. t Let c be a positive real number and let k be a
Let
rational number with positive denominator.
rational c In
In t
k () is defined to be the number c radical notation, t
k c= c=
k t ( c)
k t 1
tk = c 1
k t Laws of Exponents
Laws
1. c c = c
r 3. s r c
r −s
2. s = c
c r+s rs (c ) = c rs r r 4. c
c
5. = r
d
d ( cd ) 6. c −r if c ≠ 1 and d ≠ 1,
c r = c s iff r = s
c = d iff c = d
r r r =c d
r 1
=r
c r Joke Time
Joke
What
What are eyeglasses good for?
for?
division What
What do you get if you
divide the circumference of
a jackolantern by its
diameter?
diameter?
pumpkin pi ...
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 Winter '11
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 Calculus, Logarithmic Functions

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