logₐ(x).
log_b(x) is the exponent y such that b^y = x. Any-base log = ln(x) / ln(b).
Common bases: 10 (common log), e ≈ 2.718 (natural log).
Logarithms are the inverse operation of exponentiation, the same way subtraction inverts addition — which is exactly why they're the standard tool for solving equations where the unknown sits in the exponent.
log₁₀(1000) = 3, because 10³ = 1000.
Calculus, growth/decay problems, and continuous compounding — the base e makes derivatives clean.
Undefined in real numbers; complex in general. This tool expects positive arguments.
Because computers work in binary, log base 2 directly answers questions like 'how many bits are needed to represent this number,' making it the natural choice in that field.