What Is a Logarithm? Base 10, Base e and Base 2 Explained
A logarithm is the reverse of a power. This guide explains what that means and when each base is used.
What is the Logarithm Calculator?
Pick a base and enter a positive number. The logarithm answers the question: to what power must I raise the base to get this number? Base 10 is common in science, base e is the natural logarithm used in growth and decay, and base 2 is common in computing.
How to use it
- Choose a base: 10, e or 2.
- Enter a positive number.
- Calculate to see its logarithm.
Worked example
Log base 10 of 1000 is 3.
What is log base 10 of 1000?
It is 3, because 10 to the power 3 is 1000. In other words, the logarithm tells you how many times you multiply the base by itself to reach your number, and here three multiplications of 10 give 1000.
Frequently asked questions
Why can I not take the logarithm of zero or a negative number?
Because no power of a positive base ever gives zero or a negative result, so those logarithms are not defined for real numbers.
What is the natural logarithm?
It is the logarithm to base e, where e is about 2.718. It shows up in compound growth, decay and many natural processes.