There are three common types of logarithms used in mathematics: Common Logarithm (base 10): The common logarithm is a logarithm with a base of 10. It is denoted as log(x) or log₁₀(x), where x is the positive number for which the logarithm is calculated. For example, log(100) = 2, as 10^2 = 100. Natural Logarithm (base e): The natural logarithm is a logarithm with a base equal to the mathematical constant e, which is approximately 2.71828. It is denoted as ln(x) or logₑ(x), where x is the positive number for which the logarithm is calculated. For example, ln(e) = 1, as e^1 = e. Binary Logarithm (base 2): The binary logarithm is a logarithm with a base of 2. It is commonly used in computer science and information theory, especially in analyzing algorithms and data structures. It is denoted as log₂(x), where x is the positive number for which the logarithm is calculated. For example, log₂(8) = 3, as 2^3 = 8. These three types of logarithms have specific applications in various mathematical fields and are widely used in calculations, problem-solving, and analysis.