Precalculus 5.4 Logarithmic Functions
Objective: able to switch b/w logarithmic & exponential statements; evaluate logarithmic expressions; determine domain &
range; graph & solve logarithmic equations
Find the inverse function of
f (x) = a
x
.
The logarithmic function to the base
a
, where
a
> 0 and
a
≠1, is denoted by
y = log
a
x
(read as “
y
is the
logarithm to the base
a
of
x
”) and is defined by
y = log
a
x
if and only if
x = a
y
.
The domain of the logarithmic function
y = log
a
x
is
x
> 0.
1. Change the exponential expression 16 = 4
2
to an equivalent logarithmic expression.
2. Change the logarithmic expression
2
9
1
log
3
−=
to an equivalent exponential expression.
3. Find the exact value of
log
5
125
.
4. Find the domain of
H (x) = log
5
x
3
.
5. Find the domain of
G (x) = log
3
−1x
x
.
