AMCAT DETAILS brings you the questions on the tOptionic of
Logarithms from Quantitative Section of AMCAT exam. Prepare well and Get
Placed.

Question: If logx (0.1) = -1/3, then the value of x is -

(1): 10

(2): 100

(3): 1000

(4): 1/1000

(5): None of these

Answer :- (3)

Question: If ax = by, then :-

(2): log(a) / log(b) = x/y

(3): log(a) / log(b) = y/x

(4): None of these

(5): None
of these

Answer : (3)

Question: If log8 x + log8 (1/6) = 1/3 then, the value of x will be:

(1): 12

(2): 16

(3): 18

(4): 24

(5): None of these

Answer: (1)

Question: If log x + log y
= log (x + y), then which statement follows:

(1): x = y

(2): xy=1

(3): y = (x-1)/x

(4): y = x/(x-1)

(5): None of these

Answer: (4)

(1): -(1 + a)

(2): (1 + a)-1

(3): a/10

(4): 1/10a

(5): None of these

Answer: (1)

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Question: If log{(a+b)/3} = 0.5(log a + log b), then the
correct relation between a and b will be:

(1): a2+b2 = 7ab

(1): a2+b2 = 7ab

(2): a2-b2 = 7ab

(3): (a+b)2 = 2

(4): (a+b)/3 = (1/2)(a+b)

(5):
None of these

Answer: (1)

Question: If log x = log 3
+ 2 log 2- (3/4) log 16. The value of x will be:

(1): 1/2

(1): 1/2

(2): 1

(3): 3/2

(4): 2

(5): None of these

Answer: (3)

Question: If log x =(1/2) log y = (1/5) log z, the value
of x4y3z-2 will be:

(1): 0

(1): 0

(2): 1

(3): 2

(4): 3

(5): None of these

Answer:
(2)

Question: If log10000 x =
-1/4, then the value of x is:

(1): 1/100

(2): 1/10

(3): 1/20

(4): none of these

Answer: (2)

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Question: The value of
3-1/2 log3(9) will be:

(1): 3

(2): 1/3

(3): 2/3

(4): none of these

Answer: (2

Question: loge xy - loge
|x| is equal to:

(1): loge x

(2): loge |x|

(3): - loge x

(4): none of these

Answer: (4)

Question: The value of (loga n) / (logab n) is equal to:

(1): 1 + loga b

(2): 1 + logb a

(3): loga b

(4): logb a

(5): None of these

Answer: (1

Question: If (a4 - 2a2b2 + b4)x-1 = (a-b)2x (a+b)-2,
then the value of x will be :

(1): (a - b) / (a + b)

(2): log (a2 - b2)

(3): log (a + b) / log (a - b)

(4): log (a - b) / log (a + b)

(5): None of these

Answer: (4

Question: If a, b, and c are in geometric progression
then loga n, logb n and logc n will be in:

(1): AP

(1): AP

(2): GP

(3): HP

(4): None of these Option

Answer: (3

Question: What will be the value
of antilog10100?

(1): 2

(2): 10100

(3): 100

(4): 10

(5): None of these

Answer: (2

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Question: If antilog x 5 =
30, then what can you tell about x?

(1): x is a number between 1 and 2

(2): x is 305

(3): x is a number between 2 and 3

(4): None of these

Question: If x is increased by a given constant
number every time, y doubles and z becomes three times. How will log(y) and log(z) behave
as x is increased by the same constant number?

(1): Both will grow linearly with
different slope

(2): Both will grow linearly with same slopes

(3): y will grow linearly, while z will not grow

(4): z will grow linearly, while y
will not grow

(5): None of these

Answer: (1)

Question: If x triples every
second. How will log2x change every second?

(1): It will double every second

(2): It will triple every second

(3): It increases by a constant amount every second.

(4): None of these

(5): None of these

Answer: (3)

Question: When f(x) grows
exponentially with x, how does f(log(x)) grow?

(1): grow Exponentially

(2): grow Linearly

(3): grow Quadratically

Answer: (2)

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Question: What will be the value
of log512 8?

Option 1: 3

Option 2: 1/3

Option 3: -3

Option 4: -1/3

Option 5: None of these

Answer: (2

Question: What will be the value
of log7 (1/49)?

Option 1: 2

Option 2: 1/2

Option 3: -1/2

Option 4: -2

Option 5: None of these

Answer: (4

Question: It is given that log64 x = 2/6, then , the value of
x will be?

Option 1: 2

Option 1: 2

Option 2: 4

Option 4: 8

Option 5: None of these

Answer: (2

Question: If 7x = 85, the the value of x will be?

Option 1: log785

Option 2: log857

Option 3: log107

Option 4: log1085

Option 5: None of these

Answer: (1

Question: When log102 = 0.3010, then the number of digits in 264 will be:

Option 1: 19

Option 1: 19

Option 2: 20

Option 3: 18

Option 4: None of these

Answer: (2

Question: What is the value of log110?

Option 1: 1

Option 3: 0

Option 4: it tends to infinity

Option 5: None of these

Answer: (4

Question: What will be the value of log100 ?

Option 1: 0

Option 2: 10

Option 3: 1

Option 4: Not defined

Option 5: None of these

Answer: (4

Question: The value of log3 (-9)?

Option 1: 3

Option 1: 3

Option 2: 1/3

Option 3: -3

Option 4: Not defined

Answer: (4

Question: Sameer multiplies
a number by 10, the log (to base 10) of this number will change in what way?

Option 2: Increase by 1

Option 3: Multiplied by 10

Option 4: None of these

Option 5: None of these

Answer: (2

Question: Logarithm of a very small positive number tends to:

Option 1: 0

Option 2: negative infinity

Option 1: 0

Option 2: negative infinity

Option 3:
positive infinity

Option 4: 1

Option 4: 1

Option 5: None of these

Answer: (2

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Question:
If there are n numbers and they are in geometric progression, then the logarithm of the number
will be in which of the following?

Option 1: Geometric Progression

Option 2: Arithmetic Progression

Option 3: Harmonic Progression

Option 4: None of these

Answer: (2

Question:
Which of the following expression is same as log(a + b) ?

Option 1: log a +
log b

Option 2: log a * log b

Option 3: log a -
log b

Option 4: None of these

Answer: (4

Question:
What will be the value of log3 (1/9) + log 9 81 ?

Option 1: 2

Option 1: 2

Option 2: -2

Option 3: 0

Option 4: 4

Option 5: None of these

Answer: (3

Question:
What will be the value of log3 1.5 + log3 6 ?

Option 1: 2

Option 1: 2

Option 2: 2.7

Option 3: 1.8

Option 4: None of these

Answer: (1

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Question: log8 x is equal to?

Option 1: log2 (x/3)

Option 2: log2 (3x)

Option 3: (log2x)/ 3

Option 4: None of these

Option 5: None of these

Answer: (3

Question:
If there are n numbers and they are in arithmetic progression, then, the logarithm of the number
will be in which of the following?

Option 1: Exponentially

Option 2: Linearly

Option 3: Quadratically

Option 4: None of
these

Option 5: None of these

Answer: (4

Question: What will be the value
of log20 1 ?

Option 1: 0

Option 2: 1

Option 3: 20

Option 4: None of these

Option 5: None of these

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