Logarithm Test

Result

Logarithm Test - 1

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Weekly Quiz Competition

Question 1
3 / -1

Which of the following statements is not correct?

A
log₁₀ 10 = 1

B
log (2 + 3) = log (2 x 3)

C
log₁₀ 1 = 0

D
log (1 + 2 + 3) = log 1 + log 2 + log 3
Solution
Since log_a a = 1, so log₁₀ 10 = 1.
log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3
∴ log (2 + 3) ≠ log (2 x 3)
Since loga 1 = 0. so logio 1 = 0.
log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.
So. option (b) is incorrect.
Question 2
3 / -1

If log 2 = 0.3010 and log 3 = 0.4771, the value of log₅ 512 is:

A
2.870

B
2.967

C
3.876

D
3.912

Solution
Question 3
3 / -1

A

B
1/4

C
1/2

D
1/8

Solution
Question 4
3 / -1

If log 27 = 1.431, then the value of log 9 is:

A
0.934

B
0.945

C
0.954

D
0.958

Solution

Given, log 27 = 1.431
⇒ log (3³) = 1.431
⇒ 3 log 3 = 1.431
⇒ log 3 = 0.477
∴ log 9 = log (3²) = 2 log 3
⇒ (2 x 0.477) = 0.954
Question 5
3 / -1

A
a + b = 1

B
a - b = 1

C
a = b

D
a² - b² = 1

Solution
Question 6
3 / -1

If log₁₀ 7 = a, then is equal to :

A
- (1 + a)

B
(1 + a)^-1

C
a/10

D
1/10a

Solution

⇒ - log₁₀ (7 x 10)
⇒ - (log₁₀ 7 + log₁₀ 10)
⇒ - (a + 1)
Question 7
3 / -1

If log₁₀ 2 = 0.3010, then log₂ 10 is equal to:

A

B

C
0.3010

D
0.6990

Solution
Question 8
3 / -1

If log₁₀ 2 = 0.3010, the value of log₁₀ 80 is:

A
1.6020

B
1.9030

C
3.9030

D
None of these

Solution

log₁₀ 80 = log₁₀ (8 x 10)
⇒ log₁₀ 8 + log₁₀ 10
⇒ log₁₀(2³) + 1
⇒ 3 log₁₀ 2 + 1
⇒ (3 x 0.3010) + 1
⇒ 1.9030
Question 9
3 / -1

If log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1, then x is equal to:

A
1

B
3

C
5

D
10

Solution

log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1
⇒ log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + log₁₀ 10
⇒ log₁₀ [5 (5x + 1)] = log₁₀ [10(x + 5)]
⇒ 5(5x + 1) = 10(x + 5)
⇒ 5x + 1 = 2x + 10
⇒ 3x = 9
⇒ x = 3.
Question 10
3 / -1

The value of is:

A
0

B
1

C
5

D
60

Solution

Given expression = 1/log₆₀ 3 + 1/log₆₀ 4 + 1/log₆₀ 5
= log₆₀ (3 x 4 x 5)
= log₆₀ 60
= 1.