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

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

Multiple choice taylor's and maclaurin's series applications of differential calculus maths

The fourth term in Taylor series of $\log\ x$ centered at $a=1$ is?

  1. $\dfrac{(x-1)^3}{3}$
  2. $\dfrac{(x-1)^2}{2}$
  3. $-\dfrac{(x-1)^4}{4}$
  4. $(x-1)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The taylor series expansion of $\log x$ is $f(x) = \ln(x)$

$ = \left(x-1\right)-\dfrac{1}{2}\left(x-1\right)^2 + \dfrac{1}{3} \left(x-1\right)^3-\dfrac{1}{4} \left(x-1\right)^4 + \cdots$ $ f(x) $
$= \displaystyle\sum\limits _{n=1}^{\infty} \left[\frac{\left(-1\right)^{n+1}}{n}\left(x-1\right) ^n\right] $