Use transformations to graph the function. Determine the .... Change the
exponential expression to an equivalent expression involving a logarithm. 16) 42
= x.
College Algebra
Exponential & Logarithmic Functions Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. 1) f(x) = -2 x+3 + 4 1)
A) domain of f: (- , ); range of f: (-4, ); horizontal asymptote: y = 4
B) domain of f: (- , ); range of f: (- , 4); horizontal asymptote: y = 4
C) domain of f: (- , ); range of f: (- , -4); horizontal asymptote: y = -4
D) domain of f: (- , ); range of f: (- , -4); horizontal asymptote: y = -4
1
2) f(x) = 5 (x - 3)
2)
A) domain of f: (- , ); range of f:(0, ) horizontal asymptote: y = 0
B) domain of f: (- , ); range of f:(0, ) horizontal asymptote: y = 0
C) domain of f: (- , ); range of f:(- , 0) horizontal asymptote: y = 0
D) domain of f: (- , ); range of f:(- , 0) horizontal asymptote: y = 0
2
3) f(x) = 4 -x + 5
3)
A) domain of f: (- , ); range of f:(4, ) horizontal asymptote: y = 4
B) domain of f: (- , ); range of f:(4, ) horizontal asymptote: y = 4
C) domain of f: (- , ); range of f:(5, ) horizontal asymptote: y = 5
D) domain of f: (- , ); range of f:(5, ) horizontal asymptote: y = 5
3
Graph the function. 4) f(x) = 3 x
4)
A)
B)
C)
D)
4
5) f(x) =
5 x 4
5)
A)
B)
C)
D)
Solve the equation. 6) 21 + 2x = 32 A) {4}
7) 18x = 1 A) {1}
B) {2}
C) {16}
D) {-2}
6)
7)
1 B) { } 18
C) {0}
5
D)
1 8) 3-x = 9
8)
A) {2}
B)
1 2
C)
1 3
D) {-2}
1 9) 27 - 3x = 4
9)
A) {-3}
B) {1}
C)
1 2
D) {3}
1 10) 2x = 16
A)
10)
1 4
11) 2x = 16 A) {5}
B) {-4}
C)
1 8
D) {4}
B) {4}
C) {8}
D) {3}
C) {3}
1 D) 4
12) 4(3x - 7 ) = 16 A) {4}
13)
B) {-3}
11)
12)
1 x = 216 6
A) {-3}
14) 2x2 - 3= 64 A) {6} 15) (ex)x · e45 = e14x A) {-9, -5}
13) 1 3
B) {3}
C) -
D)
B) {3}
C) { 35, -
14)
B) {9}
35}
C) {9, 5}
x
4=2
17) ex = 9 A) ln x = 9
B) log
4
2=x
C) log
2
x=4
C) logx e = 9
B) ln 9 = x
D) {3, -3} 15)
D) {5}
Change the exponential expression to an equivalent expression involving a logarithm. 16) 42 = x A) log
1 3
D) log
4
x=2
D) log9 x = e
Change the logarithmic expression to an equivalent expression involving an exponent. 18) log x = 2 4 A) 42 = x B) x2 = 4 C) 4x = 2 D) 24 = x
6
16)
17)
18)
19) log
16 = x 2 A) 16x = 2
19) B) x2 = 16
C) 162 = x
Graph the function and its inverse on the same Cartesian plane. 20) f(x) = log4 x
A)
B)
C)
D)
7
D) 2x = 16
20)
21) f(x) = log1/4 x
21)
A)
B)
C)
D)
8
Graph the function. 22) f(x) = 2 - ln x
22)
A)
B)
C)
D)
9
23) f(x) = 2 ln x
23)
A)
B)
C)
D)
10
24) f(x) = 2 - ln(x + 4)
24)
A)
B)
C)
D)
Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. 25) log9 9 5 A) 9
26) ln e 6 A) 6 27) log2 14 - log2 7 A) 2
B) 1
C) 45
25)
D) 5
26) B) 36
C) 6
D) e 27)
B) 1
C) 14
11
D) 7
28) log4 24 - log4 6 A) 6
28) B) 24
29) log3 30 · log30 9
C) 4
D) 1 29)
A) 3
B) 2
30) 10log 30 - log 6 A) log 24
C) 9
B) 30
D) 30
C) 5
D) 100,000
Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b. 31) ln 10 A) a - b B) ab C) ln a + ln b D) a + b 32) ln 20 A) 2a + b
B) 2a + 2b
C) 4b
C) log
18
18
13 +
1 log r - log s 18 18 2
(13 r) - log
18
B) log D) log
s
18 18
33)
s - log 13 ·
31)
32)
D) a + b
Write as the sum and/or difference of logarithms. Express powers as factors. 13 r 33) log 18 s A) log
30)
18
13 -
1 log r 18 2
1 log m ÷ log s 18 18 2
2
34) log
5 3 q2 p
A) log C)
3
34) 5 - log
3
q - log p 3
B)
1 log 5 - 2 log q - 2 log p 3 3 3 2
D) 2 log 5 - 2 log q - log 2 3 3 3
Express as a single logarithm. 35) ( log x - log y) + 3 log z a a a xz 3 A) log B) log xz3 y a y a x + 5 log (x - 6) 6 6 A) 15 log x(x - 6) 6
1 log 5 - 2 log q - log p 3 3 3 2
35) C) log
a
3xz y
D) log
x a z3 y
36) 3 log
36) B) log
6
x(x - 6)15
C) log
6
x3(x - 6)5
D) log
6
x(x - 6)
Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. 37) log 0.638 37) 2 A) -0.648 B) -1.542 C) -0.195 D) 3.135 38) log
3.3 4.5 A) 1.260
38) B) 0.794
C) 0.733 12
D) 0.519
Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 39) log7.2 299 39) A) 41.53
B) 0.35
40) log5.3 3.3 A) 0.52
C) 2.89
40) B) 0.62
C) 1.40
Solve the equation. 41) log (3x) = log 2 + log (x - 1) 2 1 A) B) 5 2 42) log
2
D) 2.48
(5x + 8) = log
2
D) 0.72
41) C) 2
D) - 2
(5x + 3)
A) {0}
42)
B) {5}
C)
(x + 4) + log (x - 2) = 2 4 4 A) {4} B) {4, -6}
11 5
D)
43) log
44) 2(7 + 3x) =
43) C) {5}
D) {-6}
1 4
44)
A) {-3}
45) 3 · 52t - 1 = 75 13 A) 10
B) {3}
C)
1 2
D) {1}
B) {3}
1 C) 2
3 D) 2
Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. 3 x = 21 - x 46) 5 A) ln
C)
3 - ln 2 5
ln 2 3 ln + ln 2 5
ln
-1.204
B)
3.802
D)
13
3 + ln 2 5 ln 2
ln 6 ln 10
0.778
0.263
45)
46)
