Question

Question 1 (1 point)

(07.03)
Evaluate log3 9. (1 point)

a
2

b
3

c
0.33

d
0.5

Question 2 (1 point)
(07.03)
Evaluate log8 12. (1 point)

a
0.84

b
0.67

c
1.50

d
1.19

Question 3 (1 point)
(07.03)
Evaluate ln 7. (1 point)

a
0.51

b
1.95

c
0.85

d
1.61

Question 4 (1 point)
(07.03)
Write log4 14 as a logarithm of base 3. (1 point)

a
log base 4 of 3 over log base 14 of 3

b
log base 14 of 3 over log base 4 of 3

c
log base 3 of 4 over log base 3 of 14

d
log base 3 of 14 over log base 3 of 4

Question 5 (1 point)
(07.03)
Write log6 5 as a logarithm of base 4. (1 point)

a
log base 4 of 5 over log base 4 of 6

b
log base 4 of 6 over log base 4 of 5

c
log base 5 of 4 over log base 6 of 4

d
log base 6 of 4 over log base 5 of 4

Question 6 (1 point)
(07.03)
Solve log4 (y − 9) + log4 3 = log4 81. (1 point)

a
y = 30

b
y = 36

c
y = 87

d
y = 108

Question 7 (1 point)
(07.03)

Simplify 5 log2 k − 8 log2 m + 10 log2 n. (1 point)

a
7 log2 (k − m + n)

b
7 log2kn over m

c
log250 kn over 8 m

d
log2k to the fifth power n to the tenth power over m to the eighth power

Question 8 (1 point)
(07.03)
Solve 2 log x = log 36. (1 point)

a
x = ±6

b
x = 6

c
x = 18

d
x = 72

Question 9 (1 point)
(07.03)
Solve 4 log12 2 + log12 x = log12 96. (1 point)

a
x = 88

b
x = 80

c
x = 12

d
x = 6

Question 10 (1 point)
(07.03)
Solve 2 log2 2 + 2 log2 6 − log2 3x = 3. (1 point)

a
x = 2

b
x = 6

c
x = 16

d
x = 18

Answer 1

• 1. a, 2. d, 3. b, 4. d, 5. a, 6. b, 7. d, 8. a, 9. d, 10. b

Explanation:

Question 1

• log3 9 = log 3 3² = 2

Question 2

• log8 12 = log 12/log 8 = 1.19

Question 3

• ln 7 = log 7 / log e = 1.95

Question 4

• log4 14 as a logarithm of base 3
• log4 14 = log3 14/ log3 4

Question 5

• log6 5 as a logarithm of base 4
• log6 5 = log4 5/ log4 6

Question 6

• log4 (y − 9) + log4 3 = log4 81
• log4 (3y - 27) = log4 81
• 3y - 27 = 81
• 3y = 108
• y = 36

Question 7

• 5 log2 k − 8 log2 m + 10 log2 n
• log2 k^5 - log2 m^8 + log2 n^10 =
• log2 (k^5n^10/m^8)

Question 8

• 2 log x = log 36 log x^2 = log 36
• x^2 = 36
• x = √36
• x = ± 6

Question 9

• 4 log12 2 + log12 x = log12 96 log12 16x = log12 96
• 16x = 96
• x = 6

Question 10

• 2 log2 2 + 2 log2 6 − log2 3x = 3
• log2 (4*36/3x) = 3
• 48/x = 2^3
• 48/x = 8
• x = 48/8
• x = 6