Find the logarithm of a value to any base, with natural, base-10, and base-2 logs alongside. Enter the value and base.
Usage Tip
log base 10 of a number is roughly its digit count minus one: 1000 has 4 digits and a log of 3.
The exponent the base is raised to in order to give x
The change-of-base formula computes any base from natural logs.
Natural log (base e), base 10, and base 2 are always shown.
Logs turn multiplication into addition.
A logarithm answers the question of what power a base must be raised to in order to produce a given value. The base 10 logarithm of 1000 is 3 because 10 to the third power is 1000, and the base 2 logarithm of 8 is 3 because 2 cubed is 8. The natural logarithm uses the constant e, about 2.718, as its base.
Logarithms are defined only for positive values, and the base must be positive and not equal to 1. To change bases, divide the logarithm of the value by the logarithm of the new base. Logs turn multiplication into addition, which is why they appear in decibels, pH, earthquake magnitudes, and compound growth calculations.