Logarithm (logₐx)
Calculate a logarithm with any base. With graph, rules and real-world examples.
Co je general logarithm
The logarithm logₐx answers the question “to what power must I raise the base a to get the number x?”. It is the inverse of exponentiation: if aʸ = x, then logₐx = y.
Where it is used in practice
- Solving equations where the unknown is in the exponent (e.g. how long until savings double).
- Converting between logarithmic scales (pH, decibels, the Richter scale).
- Simplifying complex calculations – a logarithm turns multiplication into addition.
Good to know
The base a must be positive and not equal to 1, the argument x must be positive. The logarithm of a negative number or zero does not exist.
Logarithm and power are inverse operations
The logarithm is the inverse function of the power. Picturing it this way makes logarithms much easier to understand: logₐx = y ⟺ aʸ = x. For example log₂8 = 3, because 2³ = 8. The logarithm thus “unpacks” the exponent.
Rules of logarithms
In detail with examples: rules of logarithms.
Tip: a logarithm turns multiplication into addition – which is why logarithm tables and slide rules were once used to multiply large numbers quickly.