Section 4.2 The Natural Exponential Function
It is known that
(
)x
1
1+
2.7182818284590452353602874713526624977572470936.
x
as x . We denote this number by e.
(
)x
1
1+
x
Value
x
1
21
2
10
1.110
2.59
Section 4.3 Logarithmic Functions
DEFINITION: Let a be a positive number with a = 1. The logarithmic function with base
a, denoted by loga , is dened by
loga x = y
ay = x
So, loga x is the exponent to
Section 4.6 Modeling with Exponential and Logarithmic
Functions
Many processes that occur in nature, such as population growth, radioactive decay, heat diusion, and numerous others, can be modeled usi
Section 4.5 Exponential and Logarithmic Equations
Exponential Equations
An exponential equation is one in which the variable occurs in the exponent.
EXAMPLE: Solve the equation 2x = 7.
Solution 1: We
Section 4.4 Laws of Logarithms
LAWS OF LOGARITHMS: If x and y are positive numbers, then
1. loga (xy ) = loga x + loga y.
()
x
2. loga
= loga x loga y.
y
3. loga (xr ) = r loga x where r is any real n
Section 6.4 Inverse Trigonometric Functions and Right
Triangles
DEFINITION: The inverse sine function, denoted by sin1 x (or arcsin x), is dened to be
the inverse of the restricted sine function
sin x
Section 4.1 Exponential Functions
DEFINITION: An exponential function is a function of the form
f (x) = ax
where a is a positive constant.
( 1 )x
x
( 10 )3
1
-3
= 103 = 1000
( 10 )2
1
-2
= 102 = 100
(