Logarithms
Solve logarithms and explore the log curve interactively
About this calculator
The Logarithm Calculator solves for the result, argument, or base of any logarithm. Supports natural log (ln), log base 10, and any custom base. Enter two known values to instantly find the third — ideal for students, scientists, and engineers working with exponential growth, decibels, or pH.
How to use the logarithm calculator
- Pick what to solve for: the result, the argument, or the base.
- Enter the two known values (for example, base and argument).
- Read the third value as the result.
- Verify on the log curve visualization.
Common examples
- log₂(8) = 3, because 2³ = 8
- log₁₀(1,000) = 3, because 10³ = 1,000
- ln(e²) = 2, because e² = e²
- log₅(125) = 3, because 5³ = 125
- log base 4 of 64 = 3, because 4³ = 64
Frequently asked questions
What is a logarithm?
A logarithm answers the question 'what power do I raise the base to in order to get this number?'. If b^x = y, then log base b of y equals x. The natural log (ln) uses base e ≈ 2.71828; log base 10 is the common log.
Which values can I solve for?
The calculator can solve for any one of the three quantities: the result (the exponent), the argument (the number inside the log), or the base. Enter the two values you know and the calculator finds the third.
Why must the base be positive and not equal to 1?
Logarithms are defined only for positive bases other than 1. Base 1 would make every power of the base equal 1, so the function would not be invertible. Negative bases produce complex results, which are out of scope for v1.
When does solve-base have no solution?
If you ask for the base that turns argument 1 into a nonzero result, no positive base works (since any base raised to a power gives 1 only when the exponent is 0). The calculator surfaces these cases as no-solution or non-unique states instead of guessing.