Logarithm and Change of Base
=
Tap a term to see what it means, or .
Calculate
Example: starting from 1 and doubling each time, how many doublings does it take to reach 1,000? It is the logarithm of 1,000 in base 2. Change the values to work out your own case.
Step by step
What each term means
- Logarithm in Base b
- The exponent that takes b to x: if b to the power L gives x, then log_b x = L. It answers how many times to multiply b by itself.
- Natural Log of x (ln x)
- The logarithm in base e ≈ 2.718, the one in calculators and programming languages. Any base works here, as long as it is the same above and below.
- Natural Log of the Base (ln b)
- The scale factor: dividing by ln b converts from base e to base b. Logarithms in different bases are proportional.