Document for Logarithm - JEE Revision Notes

Logarithm is an important concept in mathematics and finds its application in various fields. In JEE, logarithm plays a crucial role and candidates need to have a thorough understanding of the concept to solve problems efficiently. Here is a JEE revision note on logarithm:

Introduction to Logarithm:
- Logarithm is the inverse function of exponentiation.
- It represents the power to which a base must be raised to produce a given number.
- It is denoted by logb(x), where b is the base, x is the argument, and y is the value of logarithm.

Properties of Logarithm:
- logb(1) = 0
- logb(b) = 1
- logb(xy) = logb(x) + logb(y)
- logb(x/y) = logb(x) - logb(y)
- logb(x^n) = nlogb(x)

Common Logarithm:
- The common logarithm is the logarithm with base 10.
- It is denoted by log(x) or log10(x).
- It gives the power to which 10 must be raised to produce a given number.

Natural Logarithm:
- The natural logarithm is the logarithm with base e.
- It is denoted by ln(x).
- It gives the power to which e must be raised to produce a given number.

Logarithmic Functions:
- Logarithmic functions are functions of the form f(x) = logb(x).
- They are the inverse functions of exponential functions.
- They have a vertical asymptote at x = 0.

Applications of Logarithm:
- Logarithm is used in calculating pH, sound intensity, earthquake magnitude, etc.
- It is used in computer science, finance, and engineering.
- It is used in cryptography to secure data.

Conclusion:
Logarithm is an important concept in mathematics and JEE aspirants need to have a thorough understanding of it to solve problems efficiently. This revision note covers the introduction, properties, types, functions, and applications of logarithm. JEE aspirants can use this note to revise and practice problems related to logarithm.