Logaritmeve
Logaritmeve, commonly referred to as logarithms, are mathematical functions that encode the exponent required to raise a base to obtain a given value. Formally, for a base b>0 with b≠1, the logarithm of x>0 with base b is the number y such that b^y = x. It is written log_b(x); the base e case is called the natural logarithm and written ln(x). The base 10 case is the common logarithm and historically written log(x).
Key properties include: log_b(xy) = log_b(x) + log_b(y); log_b(x^k) = k log_b(x); log_b(1) = 0; log_b(b) = 1. The change of
Logaritmeve are the inverse functions of exponentiation: y = log_b(x) is the inverse of x = b^y. Their
Common bases include base 10 (common logarithm), base e (natural logarithm, ln), and base 2 (binary logarithm).
Applications span solving exponential equations, modeling growth and decay, compound interest, pH, decibels, and logarithmic scales
Historically, logarithms were introduced in the early 17th century by John Napier, with Briggs popularizing base-10