What are Log CAT Questions?
The Logarithm concept is based on the power by which a number can be increased to get other values. Log CAT questions can be solved on the basis of the following properties:
- Power rule: Logb Mp = P Logb M
- Product rule: Logb MN = Logb M + Logb N
- Zero Exponent Rule: Loga 1 = 0
- Quotient rule: Logb M/N = Logb M – Logb N
- Change of Base Rule: Logb (x) = ln x / ln b or Logb (x) = Log10 x / Log10 b
Apart from this, the aspirants must keep in mind that the Logarithm's functions are the inverse functions of exponentiation in CAT. Note the point that is given below for conceptual clarity on the function of Log CAT Questions.
For x, a > 0, and a≠1, we can write the following expression:
y= Loga x, if x = ay
Thereby, the Logarithmic function will be as follows:
f(x) = Loga x
Go through the table that is given below to get a clear idea between Logarithms and Exponents.
52 = 25
Log5 25 = 2
102 = 100
Log10 100 = 2
43 = 64
Log4 64 = 3
Types of Log CAT Questions
In most of the cases, the aspirants have to solve two types of CAT Logarithm Questions, such as
- Natural Logarithm: This is the base “e” logarithm, in which “e” represents Euler’s constant which is approximately equal to 2.71828.
- Common Logarithm: This is the base “10” logarithm, represented as Log10.
Formulas for Log CAT Questions
There are certain formulas based on which the logarithm questions are answered in CAT exam. Here, BYJU’S Exam Prep experts have listed down some common formulas to assist you in solving the Log CAT Questions.
- Logb (mn) = Logb (m) + Logb (n)
- Logb m√n = Logb n/m
- Logb (m+n) = Logb m + Logb (1+nm)
- Logb (xy) = y Logb (x)
- Logb (m/n) = Logb (m) – Logb (n)
- Logb (m – n) = Logb m + Logb (1-n/m)
- m Logb (x) + n Logb (y) = Logb (xmyn)
Log CAT Questions: Examples
By curating the trends of CAT QA questions, our expert team has listed some examples of CAT Logarithm Questions here for the aspirants to help them understand the types and difficulty levels for Log CAT Questions.
Question 1:Find the value of x, if Log(x-1)+Log(x+1)=Log21
As we Know: Log 1= 0 we can write the following:
∴ (x-1)(x+1) = 1
Answer: x= √2 (The Log of a Negative Number is Not Defined)
Question 2:If Log (2^a × 3^b × 5^c) is the arithmetic mean of Log (2^2 × 3^3 × 5), Log (2^6 × 3 × 5^7), and Log(2 × 3^2 × 5^4), then a equals to [CAT 2017]
Solution: Log (2^a. 3^b. 5^c) = [Log (2^2.3^3.5) + Log (2^6.3.5^7) + Log (2.3^2.5^4)]/3
3 * Log (2^a. 3^b. 5^c) = Log (2^9.3^6.5^12)
Log (2^a. 3^b. 5^c)^3 = Log (2^9.3^6.5^12)
Log (2^3a. 3^3b. 5^3c) = Log (2^9.3^6.5^12)
3a = 9
The aspirants have to practice a lot to grasp Log CAT questions as these questions appear tricky if not prepared well. Attend BYJU’S Exam Prep online classes to learn the important formulas and shortcut tricks to solve CAT Logarithm Questions.
Also Read:- How much time is required to prepare for CAT?
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