Logarithm
Calculate logarithms with any base
How to use Logarithm
- 1Enter the number whose logarithm you need and pick the base, such as 10, e, or 2.
- 2Choose natural log, common log, or a custom base if available.
- 3Read the result, which is the exponent that reaches your number.
What a logarithm is
log_b(x) = y means b^y = xA logarithm is the inverse of exponentiation: it tells you what power the base must be raised to in order to equal the number.
Logarithms compress huge ranges into manageable numbers, which is why they appear in pH, decibels, and earthquake magnitude.
Frequently asked questions
What is the difference between ln and log?
ln uses base e (about 2.718); log usually means base 10 in many contexts, though some fields use log for base e.
Can I take the log of zero or a negative?
No real logarithm exists for zero or negatives; the result would require an impossible power.
How do I change the base?
Use the change-of-base rule: log_b(x) = log_k(x) / log_k(b) for any convenient base k.