MAT170 Precalculus Exam 02 - Review (Solutions)
1.
a. logb (1000) = 3
b. log7 (201) = y
c. ln(z) = 9
2.
a. 5y = 125
b. b5 = 32
c. e41 = x
3.
a. (0, ∞)
b. (−∞, 2)
c. (−2, ∞)
4.
a. 12 log(100) + 21 log(x) = 1 + 12 log(x)
b. log6 (36) − 12 log6 (x + 1) = 2 − 12 log6 (x + 1)
c. ln(e15 ) + 51 ln(x − 1) = 15 + 15 ln(x − 1)
5.
4
a. ln (x+6)
3
x
√ b. log4 xy
3 5
c. log xy4z
6.
a. x ≈ 1.09
b. x = 4 (x = −9 is not in the domain)
c. x = ln(3) ≈ 1.10 (ex = −1 does not have a real solution)
7.
a.
b.
c.
d.
A(t) = 20 000 1 + 0.051
12
0.051t
A(t) = 20 000e
$33, 269.85
t ≈ 31.56 years
12t
8.
a. − 11π
rad
6
π
b. 5 rad
c. 3π
rad.
4
9.
a. −180 000◦
b. 343.77◦
c. 157.5◦
1
MAT170 Precalculus Exam 02 - Review (Solutions)
10.
a.
b.
c.
d.
sin(θ) = − 45
tan(θ) = 43
sec(θ) = − 53
csc(θ) = − 54
11.
(0, 1)
√ !
1 3
− ,
2 2
√ √ !
2 2
−
,
2 2
√ !
1 3
,
2 2
2π
3
!
√
3 1
−
,
2 2
√ √ !
2 2
,
2 2
π
2
3π
4
π
3
90◦
120◦
5π
6
60◦
135
0◦
or
360◦
180
210◦
7π
6
!
√
3 1
−
,−
2
2
√
√ !
2
2
−
,−
2
2
◦
240
300
270◦
3π
2
√ !
1
3
− ,−
2
2
(0, −1)
2
(1, 0)
11π
6
315◦
◦
4π
3
0π
or
2π
330◦
225◦
5π
4
!
30◦
◦
π
3 1
,
2 2
π
6
45◦
◦
150◦
(−1, 0)
√
π
4
7π
4
5π
3
√
3 1
,−
2
2
√
√ !
2
2
,−
2
2
√ !
1
3
,−
2
2
!
MAT170 Precalculus Exam 02 - Review (Solutions)
12. Let
a.
b.
c.
d.
f (θ) = −5 cos 2θ +
5
π
− π8
π
4
.
5
−
π
π
3π
5π
7π
8
8
8
8
8
−5
13. Let
a.
b.
c.
d.
g(θ) = 2 sin
2
4
2
π
θ
2
−π .
2
2
3
4
5
6
−2
14. Find the exact value of each.
a. π3
b. 5π
6
c. √313
15. a = 2.16, b = 6.66, θ = 72◦
3