Logarithm is a mathematical function that is widely used in various scientific and engineering applications. It is a way of expressing the relationship between two quantities in terms of the power to which a fixed number, known as the base, must be raised to produce the given quantity.

The logarithm of a number x to the base b is denoted as logb(x) and is defined as the power to which b must be raised to produce x. In other words, if b^y = x, then logb(x) = y.

Logarithms have several important properties that make them useful in mathematical calculations. Some of these properties are:

1. The product rule: logb(xy) = logb(x) + logb(y)
2. The quotient rule: logb(x/y) = logb(x) - logb(y)
3. The power rule: logb(x^y) = y logb(x)
4. The change of base rule: logb(x) = loga(x) / loga(b)

Logarithms are used in many areas of science and engineering, such as in calculating pH levels in chemistry, measuring sound intensity in acoustics, and determining earthquake magnitude in seismology. They are also used in computer science, finance, and statistics.

In JEE Main, logarithms are an important topic that is frequently tested in the mathematics section. Students are expected to have a thorough understanding of the properties of logarithms and their applications in various fields. They should be able to solve problems involving logarithmic equations, inequalities, and graphs.

Overall, logarithms are a powerful tool in mathematics and have a wide range of applications in science and engineering. Understanding the basic concepts and properties of logarithms is essential for success in JEE Main and in many other areas of study.