The logarithms having base '10' are called

Common logarithms/briggesian logarithms

Solve as the sum and/or difference of logarithms. log18 (13√r)/s

log18 13 + 1/2 log18 r - log18 s

log18 s - log18 13 - 1/2 log18 r

log18 13 - 1/2 log18 m ÷ log18 s

Logarithm Quiz: Ultimate Exam! MCQ Trivia

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| By Ayman Tarek

Ayman Tarek

Community Contributor

Quizzes Created: 1 | Total Attempts: 880

Questions: 10 | Attempts: 881 | Updated: Jul 11, 2024

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Logarithm Quiz: Ultimate Exam! MCQ Trivia - Quiz

Logarithms are the operations done to a number to know how many times a base is raised by itself to get a given number. Calculations involving logarithms have been a little tricky form most people, and the quiz below is one way of testing out if you fully understand them. Do give the quiz a try and get to see how well you will do. All the best!

Questions and Answers

1.

The logarithms having base '10' are called
- A.
  
  Pure logarithms
- B.
  
  Common logarithms/briggesian logarithms
- C.
  
  Natural logarithms
- D.
  
  Infinite logarithms
Correct Answer
B. Common logarithms/briggesian logarithms

Explanation
The logarithms having base '10' are called common logarithms/briggesian logarithms. This is because the base 10 is commonly used in logarithmic calculations, especially in scientific and engineering fields. The common logarithm is denoted by log10 and is widely used for its convenience in calculations involving powers of 10. It is also called briggesian logarithm after the English mathematician Henry Briggs, who popularized the use of base 10 logarithms in the early 17th century.

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2.

10^-3 = 0.001 can be written in the form of logarithm as
- A.
  
  Log 1 = -3
- B.
  
  Log 0.001 = 3
- C.
  
  Log 3 =- 0.001
- D.
  
  Log 0.001 = -3
Correct Answer
D. Log 0.001 = -3

Explanation
The logarithmic form of the equation 10^-3 = 0.001 is log base 10 of 0.001 equals -3, which can be written as log 0.001 = -3. This follows from the definition of a logarithm, which states that if 10^-3 = 0.001, then log base 10 of 0.001 is -3.

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3.

The relation y = logzx implies
- A.
  
  X^y = z
- B.
  
  Z^y=x
- C.
  
  X^z=y
- D.
  
  Y²=x
Correct Answer
B. Z^y=x

Explanation
The given relation y = logzx implies that raising z to the power of y will give us x.

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4.

Solve as the sum and/or difference of logarithms. log₁₈ (13√r)/s
- A.
  
  Log₁₈ 13 + 1/2 log₁₈r - log₁₈s
- B.
  
  Log₁₈ s - log₁₈13 - 1/2 log₁₈r
- C.
  
  Log₁₈ (13√r) - log₁₈s
- D.
  
  Log₁₈ 13 - 1/2 log₁₈m ÷ log₁₈s
Correct Answer
A. Log₁₈ 13 + 1/2 log₁₈r - log₁₈s
5.

Express as a single logarithm (log_a x - log_a y) + 3log_az
- A.
  
  Log_a(xz³/y )
- B.
  
  Log_a xz³y
- C.
  
  Log_a (3xz/y)
- D.
  
  Log_a (x/z²y)
Correct Answer
A. Log_a(xz³/y )

Explanation
The given expression can be simplified using the properties of logarithms. The property states that when subtracting logarithms with the same base, we can divide the arguments of the logarithms. Applying this property, we can rewrite the expression as loga (x/y) + 3loga (z). This can be further simplified by using the property that states when multiplying a logarithm by a constant, we can raise the argument of the logarithm to that constant. Therefore, the expression can be expressed as loga (x/y) + loga (z^3). Combining the two logarithms, we get loga (xz^3/y), which matches the given answer.

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6.

Write the equation in exponential form. log₄ (1/16) = - 2
- A.
  
  2⁴ = 1/16
- B.
  
  4¹⁶ =2
- C.
  
  4^-2 = 1/16
- D.
  
  (1/16)² = 4
Correct Answer
C. 4^-2 = 1/16

Explanation
The given equation is in logarithmic form, where the base is 4 and the logarithm of 1/16 is equal to -2. To convert it into exponential form, we can rewrite it as 4^-2 = 1/16. This means that 4 raised to the power of -2 is equal to 1/16. Therefore, the answer is 4^-2 = 1/16.

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7.

Find the unknown value. log₉ (1/81) = y
- A.
  
  2
- B.
  
  -9
- C.
  
  9
- D.
  
  -2
Correct Answer
D. -2

Explanation
The given equation is asking us to find the value of y in the equation log9 (1/81) = y. In this equation, log9 represents the logarithm with base 9. The expression (1/81) is equal to 9 raised to the power of -2, which means that log9 (1/81) is equal to -2. Therefore, the unknown value y in the equation is -2.

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8.

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log₁₂₅x = 1/3
- A.
  
  1/5
- B.
  
  5
- C.
  
  1/15
- D.
  
  15
Correct Answer
B. 5

Explanation
The equation log125x = 1/3 means that 125 raised to the power of something equals x. In this case, that something is 1/3. To solve for x, we need to find the value that, when raised to the power of 1/3, equals 125. The number that satisfies this condition is 5, because 5^3 = 125. Therefore, the answer is 5.

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9.

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log₉ (5x - 3) = log₉ (3x + 7)
- A.
  
  5
- B.
  
  4
- C.
  
  2
- D.
  
  No solution
Correct Answer
A. 5

Explanation
The equation log9 (5x - 3) = log9 (3x + 7) implies that the logarithm of (5x - 3) to the base 9 is equal to the logarithm of (3x + 7) to the base 9. Since the bases are the same, the arguments must be equal. Therefore, 5x - 3 = 3x + 7. By solving this equation, we find that x = 5.

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10.

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log (2 + x) - log (x - 3) = log 2
- A.
  
  8
- B.
  
  -8
- C.
  
  3/2
- D.
  
  No solution
Correct Answer
A. 8

Explanation
The equation given is a logarithmic equation. To solve it, we can use the property of logarithms that states log(a) - log(b) = log(a/b). Applying this property to the equation, we get log((2 + x)/(x - 3)) = log(2). Since the logarithms are equal, the argument inside the logarithm should also be equal. Therefore, (2 + x)/(x - 3) = 2. By cross-multiplying and simplifying, we find that 2 + x = 2x - 6. Solving for x, we get x = 8. Therefore, the correct answer is 8.

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Jul 11, 2024

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Quiz Created by
Ayman Tarek

Logarithm Quiz: Ultimate Exam! MCQ Trivia

The logarithms having base '10' are called

10-3 = 0.001 can be written in the form of logarithm as

The relation y = logzx implies

Solve as the sum and/or difference of logarithms. log18 (13√r)/s

Express as a single logarithm (loga x - loga y) + 3loga z

Write the equation in exponential form. log4 (1/16) = - 2

Find the unknown value. log9 (1/81) = y

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log125x = 1/3

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log9 (5x - 3) = log9 (3x + 7)

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log (2 + x) - log (x - 3) = log 2

10^-3 = 0.001 can be written in the form of logarithm as

Solve as the sum and/or difference of logarithms. log₁₈ (13√r)/s

Express as a single logarithm (log_a x - log_a y) + 3log_az

Write the equation in exponential form. log₄ (1/16) = - 2

Find the unknown value. log₉ (1/81) = y

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log₁₂₅x = 1/3

Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth. log₉ (5x - 3) = log₉ (3x + 7)