Mathematics ยท Quantitative Aptitude

Logarithms

231 Questions

Logarithms are mathematical operations that determine the exponent required for a base to reach a specific number. This topic tests the application of logarithmic properties, changing bases, and solving complex equations. It is a high-yield topic for quantitative aptitude in competitive exams.

Logarithmic expressionsBase change propertiesSolving log equationsInfinite series logsCharacteristic values

Logarithms Questions

Multiple choice

What is the value of x in the equation log(x + 1) = 2?

  1. 9

  2. 10

  3. 11

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve the equation log(x + 1) = 2, we need to rewrite the equation in exponential form. The exponential form of the equation is x + 1 = 10^2 = 100. Subtracting 1 from both sides of the equation, we get x = 99. Therefore, the value of x is 9.

Multiple choice

What is the value of the expression log_2(16)?

  1. 2

  2. 3

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expression log_2(16) means the exponent to which 2 must be raised to get 16. Since 2^4 = 16, the value of the expression is 4.

Multiple choice

What is the value of the expression log_2(16)?

  1. 2

  2. 4

  3. 8

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The expression log_2(16) is equal to the exponent to which 2 must be raised to get 16. Since 2^4 = 16, the value of the expression is 4.

Multiple choice

What is the name of the mathematical operation that is the inverse of exponentiation?

  1. Logarithm

  2. Division

  3. Multiplication

  4. Subtraction

  5. Addition
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Logarithm is the mathematical operation that is the inverse of exponentiation. When you exponentiate a number, you are raising it to a power. When you take the logarithm of a number, you are finding out what power you need to raise the base number to in order to get the given number.

Multiple choice

What is the value of (\log_{10} 1000)?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The value of (\log_{10} 1000) can be found using the logarithmic property (\log_{10} 10^n = n). Since (1000 = 10^3), we have (\log_{10} 1000 = \log_{10} 10^3 = 3).

Multiple choice

Find the value of $x$ in the equation $\log_2(x + 3) = 4$.

  1. $13$
  2. $14$
  3. $15$
  4. $16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rewriting the equation in exponential form, we get $2^4 = x + 3$. Simplifying, we get $16 = x + 3$. Subtracting $3$ from both sides, we get $x = 13$. Therefore, the value of $x$ is $13$.