On this page is a logarithm calculator. Enter a logarithm base and x, and we'll compute the logarithm.
Logarithm calculator
What is a logarithm?
A logarithm answers what power y the base b must be raised to in order to get x. Rewritten, it means "how many times do I have to raise a number to equal a second number?". Stated in context, log base 2 of 64 means "What power do I raise 2 to if I want to equal 64?".
A logarithm is the opposite of an exponent. If you knew a base and an exponent, you'd be able to compute a result. When finding a logarithm, you know the base and the result and the logarithm is the exponent value you are looking to find.
Logarithm formula
The formula for a logarithm is:
log_b(x)=y
Where:
- b: the base of the equation (the number we need to raise to get the result)
- x: the argument; the number we need to raise b^y to equal
- y: the exponent or power; the number we need to raise the base to equal
Logarithm example
For example, let's say you wanted to find the log base 2 of 64. Here's how it'd look:
\log_2(64)\ or\ 2^y=64\\y=6
In this case you need to raise 2 to the 6th power to get 64.
Using the logarithm calculator
Enter two numbers to get the logarithm: the base b and the argument x. The calculator updates in real time as you type. For base e you can type the letter 'e' or use the quick button for natural log.
The Compare Across Bases section shows your value computed in binary (base 2), natural log, common log (base 10), and hexadecimal (base 16) simultaneously.
