Mathematics · 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

If log $x(\frac{5}{7}) = - \frac{1}{3}$, then the value of x is
  1. $\frac{343}{125}$
  2. $\frac{125}{343}$
  3. $\frac{-25}{49}$
  4. $\frac{-49}{25}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$log x \Big(\frac{5}{7}\Big) = - \frac{1}{3} \\ \Big(\frac{5}{7}\Big) = (x^{\frac{-1}{3}})$

Or, $x^{\frac{1}{3}}=(\frac{7}{5})$
Hence, x = $(\frac{7}{5})^3 = \frac{343}{125}$

Multiple choice

The value of log 72 is

  1. log 36 + log 36

  2. log 2 + log 144

  3. 2log 3 + 3log 2

  4. log 10

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 72 = 3x3x2x2x2

Multiple choice

log 18/6 equals

  1. log 18/log 6

  2. log 18 - log 6

  3. log 144

  4. log 18 + log 6

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

log (a/b) = log a-log b