Logarithm Calculator (Any Base)
Logarithm calculator: log of a number in any base, plus natural log and log base 10.
y = logb x
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
log_b x is the exponent that b must be raised to in order to give x. Any base works via log_b x = ln x / ln b.
Formula
y = logb x
| Symbol | Quantity | Units |
|---|---|---|
| x | Number | — |
| b | Base | — |
| y | Logarithm | — |
Worked example
Given: x = 81 · b = 3
y = ln xln b
Result: y = 4
Frequently asked questions
What is log base 3 of 81?
4, because 3⁴ = 81.