How to use the logarithm calculator
Compute natural, base-10, base-2 and custom-base logarithms. Enter number, custom base in the fields above; the natural log ln(x), log base 10, log base 2, log base b are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “log of a number”, “ln”, “change of base”, “calculate logarithm”, “find natural log ln”.
Formula
Variables
- x — Number
- b — Custom base
Worked example
With number = 1000, custom base = 5, the calculator gives natural log ln(x) ≈ 6.907755; log base 10 ≈ 3; log base 2 ≈ 9.965784; log base b ≈ 4.29203.
Frequently asked questions
What is the logarithm calculator used for?
Compute natural, base-10, base-2 and custom-base logarithms. It helps with questions such as “log of a number”, “ln”, “change of base”.
What is the formula for the logarithm calculation?
Natural log ln(x) = ln(x). Log base 10 = log10(x). Log base 2 = log2(x). Log base b = logb(x,b). Here x is number, b is custom base.
What inputs do I need for the logarithm calculator?
You need number, custom base. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the logarithm calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the logarithm result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.