# AMCAT Previous Years Questions on Logarithms

 Topics Sub- Topics Expected Ques Basic Mathematics 6 - 8 Questions Applied Mathematics 8 - 10 Questions Engineering Mathematics 8 - 10 Questions

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

Op 1: 10

Op 2: 100

Op 3: 1000

Op 4: 1/1000

Op 5:

Correct Op : 3

Ques. If ax = by, then:

Op 1: log(a/b) = x/y

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

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

Op 4: None of these

Op 5:

Correct Op : 3

Ques. If log8 x + log8 (1/6) = 1/3 then the value of x is:

Op 1: 12

Op 2: 16

Op 3: 18

Op 4: 24

Op 5:

Correct Op : 1

Ques. If log x + log y = log (x + y), then:

Op 1: x = y

Op 2: xy=1

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

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

Op 5:

Correct Op : 4

Ques. If log10 7 = a, then log10(1/70) is equal to:

Op 1: -(1 + a)

Op 2: (1 + a)-1

Op 3: a/10

Op 4: 1/10a

Op 5:

Correct Op : 1

Ques. If log{(a+b)/3} = 0.5(log a + log b), then the correct relation between a and b is:

Op 1: a2+b2 = 7ab

Op 2: a2-b2 = 7ab

Op 3: (a+b)2 = 2

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

Op 5: None of these

Correct Op : 1

Ques. If log x = log 3 + 2 log 2- (3/4) log 16. The value of x is:

Op 1: 1/2

Op 2: 1

Op 3: 3/2

Op 4: 2

Op 5: None of these

Correct Op : 3

Ques. If log x =(1/2) log y = (1/5) log z, the value of x4y3z-2 is:

Op 1: 0

Op 2: 1

Op 3: 2

Op 4: 3

Op 5: None of these

Correct Op : 2

Ques. If log10000 x = -1/4, then x is given by:

Op 1: 1/100

Op 2: 1/10

Op 3: 1/20

Op 4: none of these

Op 5:

Correct Op : 2

Ques. The value of 3-1/2 log3(9) is:

Op 1: 3

Op 2: 1/3

Op 3: 2/3

Op 4: none of these

Op 5:

Correct Op : 2

Ques. loge xy - loge |x| equals to:

Op 1: loge x

Op 2: loge |x|

Op 3: - loge x

Op 4: none of these

Op 5:

Correct Op : 4

Ques. The value of (loga n) / (logab n) is given by:

Op 1: 1 + loga b

Op 2: 1 + logb a

Op 3: loga b

Op 4: logb a

Op 5:

Correct Op : 1

Ques. If (a4 - 2a2b2 + b4)x-1 = (a-b)2x (a+b)-2, then x equals to:

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

Op 2: log (a2 - b2)

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

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

Op 5:

Correct Op : 4

Ques. If a, b, and c are in geometric progression then loga n, logb n and logc n are in:

Op 1: AP

Op 2: GP

Op 3: HP

Op 4: None of these

Op 5:

Correct Op : 3

Ques. What is the value of antilog10100?

Op 1: 2

Op 2: 10100

Op 3: 100

Op 4: 10

Op 5:

Correct Op : 2

Ques. If antilog x 5 = 30, what can you infer about x?

Op 1: x is a number between 1 and 2

Op 2: x is 305

Op 3: x is a number between 2 and 3

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Every time x is increased by a given constant number, y doubles and z becomes three times. How

will log(y) and log(z) behave as x is increased by the same constant number?

Op 1: Both will grow linearly with different slopes

Op 2: Both will grow linearly with same slopes

Op 3: y will grow linearly, while z will not

Op 4: z will grow linearly, while y will not

Op 5:

Correct Op : 1

Ques. x triples every second. How will log2x change every second?

Op 1: It will double every second

Op 2: It will triple every second

Op 3: It increases by a constant amount every second.

Op 4: None of these

Op 5:

Correct Op : 3

Ques. f(x) grows exponentially with x, how will f(log(x)) grow?

Op 1: Exponentially

Op 2: Linearly

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is the value of log512 8?

Op 1: 3

Op 2: 1/3

Op 3: -3

Op 4: -1/3

Op 5:

Correct Op : 2

Ques. What is the value of log7 (1/49)?

Op 1: 2

Op 2: 1/2

Op 3: -1/2

Op 4: -2

Op 5:

Correct Op : 4

Ques. Given that log64 x = 2/6, what is the value of x?

Op 1: 2

Op 2: 4

Op 3: 6

Op 4: 8

Op 5:

Correct Op : 2

Ques. If 7x = 85, what is the value of x?

Op 1: log785

Op 2: log857

Op 3: log107

Op 4: log1085

Op 5:

Correct Op : 1

Ques. If log102 = 0.3010, what is the number of digits in 264

Op 1: 19

Op 2: 20

Op 3: 18

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is log110?

Op 1: 1

Op 2: 10

Op 3: 0

Op 4: Tends to infinity

Op 5:

Correct Op : 4

Ques. What is log100 ?

Op 1: 0

Op 2: 10

Op 3: 1

Op 4: Not defined

Op 5:

Correct Op : 4

Ques. What is the value of log3 (-9)?

Op 1: 3

Op 2: 1/3

Op 3: -3

Op 4: Not defined

Op 5:

Correct Op : 4

Ques. The logarithm of a very small positive number will tend to which of the following?

Op 1: 0

Op 2: negative infinity

Op 3: positive infinity

Op 4: 1

Op 5:

Correct Op : 2

Ques. If n numbers are in geometric progression, the logarithm of the number will be in which of the

following?

Op 1: Geometric Progression

Op 2: Arithmetic Progression

Op 3: Harmonic Progression

Op 4: None of these

Op 5:

Correct Op : 2

Ques. Which of the following is equivalent to log(a + b) ?

Op 1: log a + log b

Op 2: log a * log b

Op 3: log a - log b

Op 4: None of these

Op 5:

Correct Op : 4

Ques. What is the value of log3 (1/9) + log 9 81 ?

Op 1: 2

Op 2: -2

Op 3: 0

Op 4: 4

Op 5:

Correct Op : 3

Ques. What is the value of log3 1.5 + log3 6 ?

Op 1: 2

Op 2: 2.7

Op 3: 1.8

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Which of the following is log8 x equivalent to?

Op 1: log2 (x/3)

Op 2: log2 (3x)

Op 3: (log2x)/ 3

Op 4: None of these

Op 5:

Correct Op : 3

Ques. If n numbers are in arithmetic progression, the logarithm of the number will be in which of the

following?

Op 1: Exponentially

Op 2: Linearly

Op 4: None of these

Op 5:

Correct Op : 4

Ques. What is the value of log20 1 ?

Op 1: 0

Op 2: 1

Op 3: 20

Op 4: None of these

Op 5:

Correct Op : 1