Download Test 3 Practice Problems

Test 3 Practice Problems
Expand the expression.
1) log 6 xy
2) log 4
11) 32 = 9
3
12) e1/3 = e
x 4 y7
5
Write an equivalent expression in exponential form.
13) log 16 = 2
4
Use the properties of logarithms to rewrite the logarithm
if possible. Assume that all variables represent positive
real numbers.
5 m
3) log 4
n
14) log
1
= -2
3 9
15) ln e4 = 4
8
4) log 4
11
16) log
Write the expression as one logarithm.
5) log 3 3 - log 3 y
6) log
3
5=
1
2
Solve the equation.
17) 36x = 6
x + log x 4 - log x 3
18)
7) 4 log (x + 3) - 5 log (x 2 + 4) +
25
1
log y
3
1 x
=4
2
19) 4(9 - 3x) = 64
Graph the function.
8) f(x) = log2 x
20) e4x - 1 = (e 2 )-x
Graph the exponential function.
21) f(x) = 2x
Write in logarithmic form.
9) 72 = 49
Use the change-of-base rule to find the logarithm to four
decimal places.
22) log 2 3
1
10) 5-3 =
125
1
23) log
5
11.08
Solve the system of linear equations.
35) x + 3y = -9
-2x + 3y = -18
Use common or natural logarithms to solve the
exponential equation symbolically.
24) 5x = 125
1
25
A) x = ln
C) x = ln 25
25) 2(1 + 2x) = 8
log 8
-2
A) x =
log 2
C) x = 2 +
26) 3(x - 1) = 11
A) x = 1 +
B) x = -
log 2
log 8
B) x =
Solve the system of nonlinear equations.
36) x2 + y2 = 113
ln 125
ln 5
x -y =1
D) x = ln 15
B) x =
log 8
1
2 log 2 2
D) x =
log 2
-2
log 8
37)
38) x 2 - 3y2 = 1
4x 2 + 3y2 = 19
Solve the system of linear equations.
39) 4x - 5y = -20
-2x - 3y = -12
log 3
log 11
State the dimensions of the matrix.
40) -9 2 4
-8 3 1
log 11
-1
log 3
C) x =
log 11
+1
log 3
D) x =
log 3
-1
log 11
xy = 30
x + y = -11
Find the values of the variables.
41)
x+3 y+4 = 6 2
7 -4
7k
Perform the matrix operation.
42) Let A = -3 6 . Find 2A.
02
Solve the equation.
27) log 3 27 = x
28) log x 100 = - 2
43) Let A = 1 3
24
29) log 5 x = 2
30) log 2
44)
1
=x
4
-3 -8
6 9
+
and B =
5 -3
-9 -1
04
-1 6
. Find 2A + B.
=
If possible, find the matrix product of AB.
45) A = -2 3 ; B = -2 0
22
-1 5
Solve the logarithmic equation symbolically.
31) 7 ln x = 10
32) ln x + ln x 5 = 6
46) A = -1 3 ; B = 0 -2 4
52
1 -3 2
33) ln 6x + ln 2x = ln 13
34) log x 9 = 7 + 3 log x
2
47) A = [-1 2 5]; B =
7
0
-3
2
9 -4 ; B =
48) A = -8
2
3 -7 6
5
Find the specified minor and cofactor for the matrix A.
-2 5 3
49) M11 and A11 if A = 4 2 -2
1 7 4
Find det A using the method of cofactors.
2 1 -1
50) A = 3 -2 -4
3 5 4
6-5 1
51) A = 0 1 6
0 0-9
State the dimensions of the matrix.
52) 8 -2 6
53) 5 0
05
Find the values of the variables.
54)
-1 5 -6 = x y -6
1 m -2
1 -7 -2
3