About the logarithm calculator
A logarithm answers the question: what power must the base be raised to in order to get this number? The logarithm of 125 to base 5 is 3, because 5³ = 125. Logarithms turn multiplication into addition and are used for decibels, pH, earthquake magnitudes and compound growth.
Use the Any base tab for a general logarithm, or one of the other tabs for the natural logarithm (base e ≈ 2.71828), the common logarithm (base 10) or the binary logarithm (base 2). Whichever you choose, the other common logarithms of the same number are shown beneath the result.
Logarithms of zero and negative numbers are not real, and the base must be positive and not equal to 1. The calculator points out which value needs to change.
Formula
- log_b(x) = y means b^y = x
- Change of base: log_b(x) = ln(x) ÷ ln(b)
- log(a × b) = log a + log b
- log(a ÷ b) = log a − log b
- log(a^n) = n × log a
Example
log₅(125) = 3 because 5³ = 125. log₁₀(1000) = 3, log₂(8) = 3 and ln(e) = 1.