Learn about logarithms, the properties of logarithms, and how they are used in solving exercises. A logarithm is a mathematical function that determines the exponent to which a given base must be raised to produce a specified number. It is denoted as logb(x), where b is the base and x is the number whose logarithm is being calculated. The logarithm of a number x to base b is the power to which b must be raised to equal x. In equation form, if y=logb(x), then x=by. Logarithms are commonly used in various scientific disciplines to simplify calculations involving exponential growth, decay, and complex multiplicative relationships.