CAT 2018 is almost here and students should concentrate on more important topics to get perfect percentile in individual sections. In quant, there are many topics to be covered and LOGARITHM is one of those. The logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. It is compulsory that question will come from this topic. So here are some properties and formulas to be focused on.
- Remainder Theorem:: Let p(x) be any polynomial of degree greater than or equal to one and ‘a’ be any real number. If p(x) is divided by (x–a), then the remainder is equal to p(a).
For example – The remainder after 2x2−5x−1 is divided by x−3
In this problem there is no need of dividing the p(x) by (x−3) rather it can be easily done by P(3):
2(3)2−5(3)−1 = 2×9−5×3−1
Hence 2 is the remainder we got from our calculations above without doing LONG DIVISION
- Factor Theorem: Let p(x) be a polynomial of degree greater than or equal to1 and ‘a’ be a real number such that p(a)=0,then(x–a)is a factor of p(x).Conversely,if(x–a) is a factor of p(x),then p(a)=0.
For example- to calculate the factor of x2−3x−4
f(4) = (4)2−3(4)−4 = 16−12−4 = 0
so (x−4) must be a factor of x2−3x−4.
Note: Let p(x) be any polynomial of degree greater than or equal to one.If leading coefficient of p(x) is 1then p(x) is called monic.
Properties of Logarithms:
The logarithm of a number contains two parts, namely ‘characteristic’ and ‘mantissa’.
1)Characteristic: The internal part of the logarithm of a number is called its characteristic.
Case I: When the number is greater than1. In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.
Case II: When the number is less than1. In this case, the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and it is negative. Instead of-1,-2etc.wewrite 1 (one bar), 2 (two bar),etc.
2)Mantissa: The decimal part of the logarithm of a number is known is its mantissa. For mantissa, we look through log table.
To Know more Concept and examples related to Logarithms, Download the Logarithms
A serious candidate should take all these steps seriously and solve all the questions has he come across, This will definitely get him/her the desired score.
Have a look at How to prepare for CAT 2018 in less than 6 months?
Enroll now in the CAT Super 50 course and get personalized mentorship from IIM and FMS alumni, Click Here