Logarithm

Question:
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.

Question:
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

Answer: Option C

Explanation:

log5 512	= log 512 log 5
	= log 29 log (10/2)
	= 9 log 2 log 10 – log 2
	= (9 x 0.3010) 1 – 0.3010
	= 2.709 0.699
	= 2709 699
	= 3.876

Question: 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.

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

[A].

699

301

[B].

1000

301

[C].

0.3010

[D].

0.6990

Answer: Option B

Explanation:

log2 10 =	1	=	1	=	10000	=	1000	.
	log10 2		0.3010		3010		301

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

[A].

0.934

[B].

0.945

[C].

0.954

[D].

0.958

Answer: Option C

Explanation:

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:
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.

Question:
If ax = by, then:

[A].

log	a	=	x
	b		y

[B].

log a	=	x
log b		y

[C].

log a	=	y
log b		x

[D].

None of these

Answer: Option C

Explanation:

ax = by

log ax = log by

x log a = y log b

	log a	=	y	.
	log b		x

Question: 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

Answer: Option B

Explanation:

(a) Since logaa = 1, so log10 10 = 1.

(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

      log (2 + 3) log (2 x 3)

(c) Since loga 1 = 0, so log10 1 = 0.

(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.

So, (b) is incorrect.

Question:
If logxy = 100 and log2x = 10, then the value of y is:

[A].

210

[B].

2100

[C].

21000

[D].

210000

Answer: Option C

Explanation:

log 2x = 10         x = 210.

logxy = 100

y = x100

y = (210)100     [put value of x]

y = 21000.

Question:
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.