Mathematics · Quantitative Aptitude

Logarithms

246 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 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 entropy of a random variable?

  1. H(X) = -∑p(x) log2 p(x)

  2. H(X) = -∑p(x) log10 p(x)

  3. H(X) = -∑p(x) log2(1 - p(x))

  4. H(X) = -∑p(x) log10(1 - p(x))
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The entropy of a random variable X is given by H(X) = -∑p(x) log2 p(x), where p(x) is the probability of the outcome x.

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 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 $13$.

Multiple choice

The logarithmic decrement ($\delta$) of a damped harmonic oscillator is:

  1. $\ln\left(\frac{A_1}{A_2}\right)$
  2. $\ln\left(\frac{A_2}{A_1}\right)$
  3. $\ln\left(\frac{x_1}{x_2}\right)$
  4. $\ln\left(\frac{x_2}{x_1}\right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The logarithmic decrement ($\delta$) of a damped harmonic oscillator is defined as the natural logarithm of the ratio of two consecutive amplitudes, $\ln\left(\frac{A_1}{A_2}\right)$, where $A_1$ and $A_2$ are the amplitudes at two consecutive peaks.