Logarithm - General Questions

The value of log₂ 16 is:

A.	1/8
B.	4
C.	8
D.	16

Answer: Option B

Explanation:

Let log₂ 16 = n.

Then, 2ⁿ = 16 = 2⁴ n = 4.

log₂ 16 = 4.

If log_x y = 100 and log₂ x = 10, then the value of y is:

A.	2 10
B.	2 100
C.	2 1000
D.	2 10000

Answer: Option C

Explanation:

log ₂ x = 10 x = 2¹⁰.

log_x y = 100

y = x¹⁰⁰

y = (2¹⁰)¹⁰⁰ [put value of x]

y = 2¹⁰⁰⁰.

If a^x = b^y, then:

A.	log a/b = x/y
B.	log a/log b = x/y
C.	log a/log b = y/x
D.	None of these

Answer: Option C

Explanation:

a^x = b^y

log a^x = log b^y

x log a = y log b

	log a	=	y	.
	log b		x

If log_x		9		= -	1	, then x is equal to:
		16			2

A.	- 3/4
B.	3/4
C.	81/256
D.	256/81

Answer: Option D

Explanation:

log_x		9		= -	1
		16			2

x^-1/2	=	9
		16

	1	=	9
	x		16

x =	16
	9

x =		16		2
		9

x =	256
	81

If log 2 = 0.30103, the number of digits in 2⁶⁴ is:

A.	18
B.	19
C.	20
D.	21

Answer: Option C

Explanation:

log (2⁶⁴)	= 64 x log 2
	= (64 x 0.30103)
	= 19.26592

Its characteristic is 19.

Hence, then number of digits in 2⁶⁴ is 20.

The value of		1	+	1	+	1		is:
		log₃ 60		log₄ 60		log₅ 60

A.	0
B.	1
C.	5
D.	60

Answer: Option B

Explanation:

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

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

A.	1
B.	3
C.	5
D.	10

Answer: Option B

Explanation:

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.

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

A.	1.6020
B.	1.9030
C.	3.9030
D.	None of these

Answer: Option B

Explanation:

log₁₀ 80	= log₁₀ (8 x 10)
	= log₁₀ 8 + log₁₀ 10
	= log₁₀ (2³ ) + 1
	= 3 log₁₀ 2 + 1
	= (3 x 0.3010) + 1
	= 1.9030.

Logarithm - General Questions

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