4.3 Logarithmic Functions
Name___________________________________
9) The graph of y = logb x passes through
Provide the missing information.
1) Given y = log x, the base is understood to
be
. Given y = ln x, the base is
understood to be
the point (1, 0) and the line
a (horizontal/vertical) asymptote.
.
10) y = logb x is called the logarithmic form
2) Given positive real numbers x and b such
that b 1, y = logb x is the
of a logarithmic equation and b y = x is
called the
form.
function base b and is equivalent to b y =
x.
11) The graph of f (x) = log4 (x + 6) - 8 is the
graph of y = log4 x shifted 6 units
3) Given y = logb x, the value y is called the
, b is called the
x is called the
(left/right/upward/downward) and
shifted 8 units
(left/right/upward/downward).
, and
.
4) The inverse of an exponential function
base b is the
function base b.
Write the equation in exponential form.
12) log 243 = b
3
5) The logarithmic function base 10 is
called the
logarithmic
13) log
function, and the logarithmic function
base e is called the
1
= -3
4 64
Write the equation in logarithmic form.
14) 83 = b
logarithmic function.
6) logb b =
because b = b.
15) 103 = 1,000
7) f (x) = logb x and g(x) = bx are inverse
16) 4-3 =
functions. Therefore, logb bx =
and b
is
log x
b
=
1
64
.
Simplify the expression.
17) log 81
8) Given y = logb x, if b > 1, then the graph
3
of the function is a(n)
(increasing/decreasing) logarithmic
function. If 0 < b < 1, then the graph is
(increasing/decreasing).
18) log
1
9
1
81
19) ln
20) log
1
32) y = -2 + log (x)
4
e6
1/2
Solve the problem.
33) Use transformations of the graph of y =
log x to graph the function.
32
5
y = log (x - 4) - 3
21) log 0.0001
5
Simplify the expression without using a calculator.
22) log 10,000,000,000
23) log
Write the domain in interval notation.
34) f (x) = log(4 - x)
1
1/2 16
35) f (x) = ln(x2 - 6x + 5)
Approximate the value of the logarithm to four
decimal places.
24) log 789
Simplify the expression.
25)
5
log (x + 4)
6 6
26) 5
log (6x + 7y)
5
2
27) ln ex + 1
28) log 1
e
Graph the function.
29) y = log x
8
30) y = ln x
a. Use transformations to graph the function.
b. Write the domain and range in interval notation.
c. Determine the vertical asymptote.
31) y = log (x + 1)
4
2
Answer Key
Testname: SECTION 4.3 EXERCISES
29)
1) 10; e
2) logarithmic
3) logarithm, base, argument
4) logarithmic
5) common; natural
6) 1; 1
7) x ; x
8) increasing; decreasing
9) x = 0; vertical
10) exponential
11) left; downward
30)
b
12) 3 = 243
1
13) 4-3 =
64
14) log b = 3
8
15) log 1,000 = 3
1
= -3
16) log
4 64
17) 4
18) -2
19) -6
20) -5
21) -4
22) 10
23) 4
24) 2.8971
31)
25) x5 + 4
26) 6x + 7y
27) x2 + 1
28) 0
b. domain: (-1, ), range (- , )
c. vertical asymptote: x = -1
3
Answer Key
Testname: SECTION 4.3 EXERCISES
32) a.
b. domain: (0, ), range (- , )
c. vertical asymptote: x = 0
33)
34) (- , 4)
35) (- , 1) (5, )
4