Logarithm Calculator
Enter a number and a base to find the logarithm, or choose the antilog option to work out what a base raised to a power comes to. The common logs are always shown too.
The number must be above zero for a logarithm, and the base must be above zero and not 1.
Worked examples
A common logarithm
log of 1000 to base 10
3
10 × 10 × 10 = 1,000.
A binary logarithm
log of 1024 to base 2
10
2 to the power of 10 is 1,024, so 1,024 needs 10 doublings from 1.
About Logarithm Calculator
A logarithm answers the question: what power must the base be raised to in order to give this number? The logarithm of 1,000 to base 10 is 3, because 10 cubed is 1,000. Logarithms turn multiplication into addition, which made them a tool for hand calculation for centuries, and today they describe anything that grows or shrinks by multiplying, from sound levels and earthquakes to acidity and interest.
This calculator finds the logarithm to any base you choose, and always shows the three most common at the same time: the natural logarithm ln, which uses the number e, the common logarithm to base 10 and the binary logarithm to base 2. You can also switch to the antilog option, which does the reverse and raises the base to the power you enter. A check line shows the base raised to your answer so you can see it return the original number.
How to use Logarithm Calculator
- Choose whether to find a logarithm or an antilog.
- Enter the number in the first box. For a logarithm it must be above zero.
- Enter the base, or type e for the natural logarithm. The base must be above zero and not 1.
- Read the result, the ln, log10 and log2 values and the check.
Common uses
- Solving equations where the unknown is in the power
- Decibel, Richter scale and pH calculations
- Working out how many times something doubles
- Finding bit lengths and powers of 2 in computing
Frequently asked questions
What is the difference between log and ln?
Log usually means the logarithm to base 10, and ln means the natural logarithm to base e, where e is about 2.71828. Both measure the same idea with a different base.
How do I find a logarithm to a base my calculator does not have?
Use the change of base rule: log to base b of x equals ln x divided by ln b. This page does this for you, so just type the base into the base box.
Why must the number be above zero?
No power of a positive base can give zero or a negative number, so the logarithm does not exist for them.
What is an antilog?
It is the reverse of a logarithm. The antilog of 3 to base 10 is 10 cubed, which is 1,000. Choose the antilog option and enter the power.
Why is the logarithm of a number between 0 and 1 negative?
A power below zero gives a fraction. For example, 10 to the power of -1 is 0.1, so the logarithm of 0.1 to base 10 is -1.