What is a Logarithm?
A logarithm is simply the inverse of an exponent. While an exponent asks, "What do I get if I multiply a base by itself X times?", a logarithm asks the reverse: "How many times must I multiply the base to get this specific number?"
Written as a logarithm, this is: log₁₀(100) = 2.
The Three Common Log Bases
Base 10 (Common Log)
Usually written simply as log(x) without a base number. It is used heavily in chemistry (pH scale), physics (Richter scale for earthquakes), and audio engineering (decibels).
Base e (Natural Log)
Written as ln(x). The base is Euler's number ($e \approx 2.718$). It is used in economics (continuous compound interest) and biology (population growth models).
Base 2 (Binary Log)
Written as log₂(x). Used almost exclusively in computer science and information theory to measure data sizes (bits and bytes) and algorithm efficiency.
What is an Antilog?
An antilogarithm is just reversing the logarithmic process to find the original number. If you know the base and the logarithm result, you calculate the antilog by raising the base to that result.
For example, if log₁₀(x) = 3, then the antilog is 10³. The original number was 1,000.