Logarithm Test

Result

Logarithm Test - 5

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Weekly Quiz Competition

Question 1
3 / -1

A
2.689

B
-0.0552

C
2.2402

D
2.702

Solution
Question 2
3 / -1

If log 2 = .301, find the number of digits in (125)²⁵.

A
53

B
50

C
25

D
63

Solution

logy = 25 log 125
= 25 [log 1000 - 3 log 2]
= 25 x (2.097)
= 52 +
Hence 53 digits.
Question 3
3 / -1

A
90

B
65

C
13

D
45

Solution

(75/35) x (49/25) x (jc/105) x (25/13) = 1 ⇒ x = 13
Question 4
3 / -1

Which one of the following is true

A
log₁₁ 1650 > log₁₃ 1950

B
lo₁₁1650 < log₁₃1950

C
log₁₁1650 = log₁₃1950

D
None of these

Solution
Question 5
3 / -1

A
2

B
3

C
0

D
None of the

Solution

x = (16/15) x (25⁵/24⁵) x (81³/80³) None of these is correct.
Question 6
3 / -1

Find the value of the logarithmic expression in the questions below.

A
1

B
n

C
0

D
2

Solution

log (aⁿbⁿcⁿ/aⁿbⁿcⁿ) = log 1 = 0
Question 7
3 / -1

A

B

C

D

Solution
Question 8
3 / -1

log₂ (9 - 2^X) = 10^{log (3-x)} Solve for x.

A
0

B
3

C
Both (a) and (b)

D
0 and 6

Solution

For x = 0, we have LHS
Log₂ 8 = 3.
RHS: 10^log3 = 3.
We do not get LHS = RHS for either x = 3 or x = 6.
Thus, option (a) is correct.
Question 9
3 / -1

Which one of the following is true

A

B

C

D
Cannot be determined

Solution
Question 10
3 / -1

log (x - 13) + 3 log 2 = log (3x + 1)

A
20

B
21

C
22

D
24

Solution
Question 11
3 / -1

log . 0867 = ?

A
log 8.67+ 2

B
log 8.67-2

C

D
-2 log 8.67

Solution

Log 0.0867 = log (8.67/100) = log 8.67 - log 100 Log 8.67 - 2
Question 12
3 / -1

log₃x = 1/2

A
3

B
√3

C
3/2

D
2/3

Solution

x = 3^1/2 = √3 .
Question 13
3 / -1

If log₁₀a = b, find the value of 10^3b in terms of a.

A
a³

B
3a

C
a x 1000

D
a x 100

Solution

log₁₀a = b ⇒ 10^b = a ⇒ By definition of logs.
Thus 10^3b = (10^b)³ = a³.
Question 14
3 / -1

log (x² - 6x + 6) = 0

A
5

B
1

C
Both (a) and (b)

D
3 and 2

Solution
Question 15
3 / -1

Find x If logx = log 1.5 + log 12

A
12

B
8

C
18

D
15

Solution

log x = log 18 ⇒ x = 18