Logarithm Calculator
Find the logarithm of a number in any base, with ln and log₁₀ shown too.
- 1
ln(x)
ln(1,000) = 6.907755 - 2
ln(b)
ln(10) = 2.302585Natural log of the base. - 3
logₐ(x) = ln(x) ÷ ln(b)
6.907755 ÷ 2.302585 = 3
Formula
How this is calculated
You supply two numbers: the value x (the argument whose logarithm you want) and the base b. The logarithm logₐ(x) is the exponent to which b must be raised to get x, so b^result = x. Because most math libraries only provide the natural logarithm (ln, base e ≈ 2.71828), the calculator applies the change-of-base formula logₐ(x) = ln(x) ÷ ln(b), dividing the natural log of x by the natural log of the base.
Alongside your custom base it always reports ln(x) (base e) and log₁₀(x) (the common log, base 10), which are simply the same change-of-base computation with b fixed to e and 10. Results are shown to six decimal places.
Logarithms are only defined for a positive argument, so x must be greater than 0, and the base must be positive and not equal to 1 (base 1 makes ln(b) = 0, which would divide by zero). The math assumes exact real-valued inputs; floating-point rounding can make results that should be whole numbers, such as log₁₀(1000) = 3, appear as 2.999999 in rare cases.
About this calculator
A logarithm answers the question: to what power must the base be raised to produce a given value? For example, log₁₀(1000) = 3 because 10³ = 1000. The natural log uses base e (≈ 2.71828) and the common log uses base 10.
This calculator uses the change-of-base formula, logₐ(x) = ln(x) / ln(b), which lets it compute a logarithm in any base from the natural logarithm. Logarithms require a positive argument and a positive base other than 1.
Frequently asked questions
ln is the natural logarithm with base e (≈ 2.718), while "log" usually means the common logarithm with base 10. Both are special cases of the general logarithm.
Logarithms are only defined for positive arguments because no real power of a positive base produces zero or a negative number.
It lets you compute a logarithm in any base using another base: logₐ(x) = log_c(x) / log_c(b). This calculator uses the natural log as base c.
Also known as
TG we-Calculate Editorial Team. (2026). Logarithm Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/logarithm-calculator
TG we-Calculate Editorial Team. "Logarithm Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/logarithm-calculator.
TG we-Calculate Editorial Team, "Logarithm Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/logarithm-calculator
@misc{wecalculate_logarithm_calculator, title = {Logarithm Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/logarithm-calculator}}, year = {2026}, note = {TG we-Calculate} }
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