Logarithm Calculator
Calculate a logarithm with any valid base.
Logarithm Calculator
How this calculator works
The logarithm log base b of x is the exponent y satisfying bʸ = x. The number must be positive, while the base must be positive and different from one.
When to use it
Use this calculator to check homework, verify a manual calculation, compare examples, and explore how changing each input affects the result. Enter all measurements in compatible units and interpret the answer within the context of your problem.
Formula and examples
The logarithm log base b of x is the exponent y satisfying bʸ = x. The number must be positive, while the base must be positive and different from one.
Can I use decimal values?
Decimal values are supported when the mathematical operation permits them. Factorials require nonnegative whole numbers.
Why might a result be undefined?
Some operations have restrictions, such as division by zero, invalid logarithm bases, or a zero leading coefficient in a quadratic equation.