Logarithm and types

A logarithm is the inverse operation to exponentiation. It determines the exponent to which a base must be raised to produce a given number. If $b^y = x$, then the logarithm is written as $\log_b(x) = y$.

There are two main types of logarithms commonly used:

• Common Logarithm: This is a logarithm with base 10. It is often written as $\log(x)$ or $\log_{10}(x)$. For example, $\log_{10}(100) = 2$ because $10^2 = 100$.

• Natural Logarithm: This is a logarithm with base $e$ (Euler's number, approximately 2.71828). It is written as $\ln(x)$ or $\log_e(x)$. For example, $\ln(e^3) = 3$ because $e^3 = e^3$.