Logarithm Study Guide for Competitive Exams

Logarithm

Q. If log10(10x) = 2, what is the value of x?

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

Solution

10x = 10^2, so x = 10.

Correct Answer: B — 100

Q. If log10(5) = a, what is log10(25) in terms of a?

A. 2a
B. a
C. a/2
D. 4a

Solution

log10(25) = log10(5^2) = 2 * log10(5) = 2a.

Correct Answer: A — 2a

Q. If log10(x) + log10(10) = 2, what is the value of x?

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

Solution

log10(x) = 2 - 1 = 1, so x = 10^1 = 10.

Correct Answer: B — 100

Q. If log10(x) = -1, what is the value of x?

A. 0.1
B. 1
C. 10
D. 100

Solution

x = 10^-1 = 0.1.

Correct Answer: A — 0.1

Q. If log10(x) = 2, what is the value of x?

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

Solution

x = 10^2 = 100.

Correct Answer: B — 100

Q. If log2(x) + log2(8) = 7, what is the value of x?

A. 32
B. 64
C. 128
D. 256

Solution

log2(x) = 7 - log2(8) = 7 - 3 = 4, so x = 2^4 = 16.

Correct Answer: B — 64

Q. If log2(x) = 5, what is the value of x?

A. 16
B. 32
C. 64
D. 128

Solution

x = 2^5 = 32.

Correct Answer: C — 64

Q. If log3(81) = x, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

81 = 3^4, so x = 4.

Correct Answer: C — 4

Q. If log4(64) = x, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

64 = 4^3, so x = 3.

Correct Answer: B — 3

Q. If log7(343) = x, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

343 = 7^3, so x = 3.

Correct Answer: A — 3

Q. If log7(49) = x, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

49 = 7^2, so x = 2.

Correct Answer: B — 2

Q. If log7(x) = 2, what is the value of x?

A. 14
B. 28
C. 49
D. 56

Solution

x = 7^2 = 49.

Correct Answer: C — 49

Q. If log7(x) = 3, what is the value of x?

A. 49
B. 21
C. 7
D. 14

Solution

x = 7^3 = 343.

Correct Answer: A — 49

Q. If logb(64) = 6, what is the value of b?

A. 2
B. 4
C. 8
D. 16

Solution

64 = b^6, so b = 64^(1/6) = 2.

Correct Answer: C — 8

Q. If logx(100) = 2, what is the value of x?

A. 10
B. 20
C. 30
D. 40

Solution

x^2 = 100, so x = 10.

Correct Answer: A — 10

Q. If logx(27) = 3, what is the value of x?

A. 3
B. 9
C. 27
D. 81

Solution

x = 27^(1/3) = 3.

Correct Answer: C — 27

Q. If logx(49) = 2, what is the value of x?

A. 5
B. 7
C. 14
D. 49

Solution

x^2 = 49, so x = 7.

Correct Answer: B — 7

Q. If logx(64) = 6, what is the value of x?

A. 2
B. 4
C. 8
D. 16

Solution

x = 64^(1/6) = 2.

Correct Answer: C — 8

Q. If logx(81) = 4, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

x = 81^(1/4) = 3.

Correct Answer: A — 3

Q. What is the value of log10(0.01)?

A. -1
B. -2
C. 0
D. 1

Solution

log10(0.01) = log10(10^-2) = -2.

Correct Answer: B — -2

Q. What is the value of log10(1)?

A. 0
B. 1
C. -1
D. undefined

Solution

log10(1) = 0 because 10^0 = 1.

Correct Answer: A — 0

Q. What is the value of log10(100)?

A. 1
B. 2
C. 3
D. 0

Solution

log10(100) = 2 because 10^2 = 100.

Correct Answer: B — 2

Q. What is the value of log10(1000)?

A. 1
B. 2
C. 3
D. 4

Solution

log10(1000) = log10(10^3) = 3.

Correct Answer: C — 3

Q. What is the value of log10(50) approximately?

A. 1.5
B. 1.7
C. 1.9
D. 2.0

Solution

log10(50) is approximately 1.7.

Correct Answer: B — 1.7

Q. What is the value of log2(1/8)?

A. -2
B. -3
C. -4
D. -5

Solution

1/8 = 2^-3, so log2(1/8) = -3.

Correct Answer: B — -3

Q. What is the value of log2(32)?

A. 4
B. 5
C. 6
D. 7

Solution

log2(32) = log2(2^5) = 5.

Correct Answer: B — 5

Q. What is the value of log2(8) + log2(4)?

A. 3
B. 4
C. 5
D. 6

Solution

log2(8) = 3 and log2(4) = 2, so 3 + 2 = 5.

Correct Answer: B — 4

Q. What is the value of log4(16)?

A. 1
B. 2
C. 3
D. 4

Solution

log4(16) = log4(4^2) = 2.

Correct Answer: B — 2

Q. What is the value of log5(25)?

A. 1
B. 2
C. 3
D. 4

Solution

log5(25) = log5(5^2) = 2.

Correct Answer: B — 2

Q. What is the value of log7(49)?

A. 1
B. 2
C. 3
D. 4

Solution

log7(49) = log7(7^2) = 2.

Correct Answer: B — 2

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