Chapter 5

107

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Unformatted text preview: exponential
equations:
 
 1 Ex:

Solve
for
t:
 ( )2 t = 9t −6 
 3 
 
 
 
 
 
 
 
 
 
 
 
 Ex:

Solve
for
x:
 272 x + 4 = 94 x 
 
 
 
 
 
 
 
 
 
 
 
 Properties
of
real
number
exponents
for
 b x , b > 0, b ≠ 1
 
 1)

If
x
is
real,

 b x 
is
a
unique
real
number














example:

 31.2 
 
 2)

If
x
is
an
integer,
 b x 
is
known

 
 
 
example:

 32 
 
 2 3)

If

x
is
rational,
 b x 
can
be
expressed
as
a
radical














example:

 3 3 = 3 32 
 
 4)

If
x
is
irrational,
approximate
 b x 
with
 b r 
where
 r ≈ x 






example
 3 2 ≈ 31.2 
 
 
 Remember:

All
the
properties
related
to
exponents
will
hold
true
for
1‐4
 
 
 
 
 The
Exponential
Function
 y = e x 

(5.2)
 
 Note:

The
base
e
is
called
the
natural
base
and
for
our
purpose...
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