AMCAT Maths Logarithms Question and Answers

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

A: 10

B: 100

C: 1000

D: 1/1000

Correct Answer : C


2. If ax = by, 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

Correct Answer : C


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

A: 12

B: 16

C: 18

D: 24

Correct Answer : A


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

A: x = y

B: xy=1

C: y = (x-1)/x

D: y = x/(x-1)

Correct Answer : D


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

A: -(1 + a)

B: (1 + a)-1

C: a/10

D: 1/10a

Correct Answer : A


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

A: a2+b2 = 7ab

B: a2-b2 = 7ab

C: (a+b)2 = 2

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

Correct Answer : A


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

A: 1/2

B: 1

C: 3/2

D: 2

Correct Answer : C


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

A: 0

B: 1

C: 2

D: 3

Correct Answer : B


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

A: 1/100

B: 1/10

C: 1/20

D: none of these

Correct Answer : B


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

A: 3

B: 1/3

C: 2/3

D: none of these

Correct Answer : B


11. loge xy – loge |x| equals to:

A: loge x

B: loge |x|

C: – loge x

D: none of these

Correct Answer : D


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

A: 1 + loga b

B: 1 + logb a

C: loga b

D: logb a

Correct Answer : A


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

A: (a – b) / (a + b)

B: log (a2 – b2)

C: log (a + b) / log (a – b)

D: log (a – b) / log (a + b)

Correct Answer : D


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

A: AP

B: GP

C: HP

D: None of these

Correct Answer : C


14. What is the value of antilog10100?

A: 2

B: 10100

C: 100

D: 10

Correct Answer : B


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

A: x is a number between 1 and 2

B: x is 305

C: x is a number between 2 and 3

D: None of these

Correct Answer : A


16. 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?

A: Both will grow linearly with different slopes

B: Both will grow linearly with same slopes

C: y will grow linearly, while z will not

D: z will grow linearly, while y will not

Correct Answer : A


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

A: It will double every second

B: It will triple every second

C: It increases by a constant amount every second.

D: None of these

Correct Answer : C


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

A: Exponentially

B: Linearly

C: Quadratically

D: None of these

Correct Answer : B


19. What is the value of log512 8?

A: 3

B: 1/3

C: -3

D: -1/3

Correct Answer : B


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

A: 2

B: 1/2

C: -1/2

D: -2

Correct Answer : D


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

A: 2

B: 4

C: 6

D: 8

Correct Answer : B


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

A: log785

B: log857

C: log107

D: log1085

Correct Answer : A


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

A: 19

B: 20

C: 18

D: None of these

Correct Answer : B


24. What is log110?

A: 1

B: 10

C: 0

D: Tends to infinity

Correct Answer : D


25. What is log100 ?

A: 0

B: 10

C: 1

D: Not defined

Correct Answer : D


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

A: 3

B: 1/3

C: -3

D: Not defined

Correct Answer : D


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

A: 0

B: negative infinity

C: positive infinity

D: 1

Correct Answer : B


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

following?

A: Geometric Progression

B: Arithmetic Progression

C: Harmonic Progression

D: None of these

Correct Answer : B


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

A: log a + log b

B: log a * log b

C: log a – log b

D: None of these

Correct Answer : D


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

A: 2

B: -2

C: 0

D: 4

Correct Answer : C


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

A: 2

B: 2.7

C: 1.8

D: None of these

Correct Answer : A


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

A: log2 (x/3)

B: log2 (3x)

C: (log2x)/ 3

D: None of these

Correct Answer : C


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

following?

A: Exponentially

B: Linearly

C: Quadratically

D: None of these

Correct Answer : D


34. What is the value of log20 1 ?

A: 0

B: 1

C: 20

D: None of these

Correct Answer : A