Logarithm Calculator — log₁₀, ln, log₂, Any Base
Find the logarithm of any positive number in common (base 10), natural (base e), binary (base 2), or any custom base — with a curve showing where your value sits.
Bonn
Result for the selected base
- 1
Argument x
100 - 2
log₁₀(x)
log₁₀(100) = 2
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log_b(x) = ln(x) / ln(b) answers "b to what power gives x?" Common (base 10) and natural (base e) logs are most widely used. Enter a positive number, pick a base, and the calculator shows common, natural, and binary results plus a log curve up to 1.6× your input for visual context.
Foirmle
How this is calculated
The logarithm log_b(x) answers the question "b raised to what power equals x?" For the common log (base 10), log₁₀(100) = 2 because 10² = 100. For the natural log, the base is Euler's number e ≈ 2.71828, and ln(x) appears constantly in calculus, growth models, and probability. For the binary log (base 2), log₂(8) = 3 because 2³ = 8 — this arises in computer science (bits, binary tree depth, information theory).
All logarithm values are computed from the natural logarithm using the change-of-base rule: log_b(x) = ln(x) / ln(b). For a custom base, enter any positive number except 1 — base 1 is excluded because 1 raised to any power equals 1, making the logarithm undefined. The stat panel always shows common, natural, and binary logs alongside the selected-base result so you can compare all three.
The input must be strictly positive; the logarithm of zero is negative infinity, and the logarithm of a negative number is not a real number (it is defined in the complex plane, but not on the real line). The plot shows the log curve up to about 1.6× your input, letting you see its characteristic shape — fast growth near zero, then gradually flattening — and exactly where your point lies.
Ceisteanna coitianta
"log" commonly means log base 10 in engineering and science, but is taken as the natural log in pure mathematics. "ln" always means the natural log (base e ≈ 2.71828). This calculator labels them explicitly to remove ambiguity.
Use the change-of-base rule: log_b(x) = ln(x) / ln(b). For example, log₅(25) = ln(25) / ln(5) ≈ 3.219 / 1.609 = 2. Enter a custom base in the calculator to compute this automatically.
As x approaches zero from the right, log(x) approaches negative infinity — there is no finite exponent to which any valid base can be raised to reach exactly zero.
Ar a dtugtar freisin
TG we-Calculate Editorial Team. (2026). Logarithm Calculator — log₁₀, ln, log₂, Any Base [Online calculator]. TG we-Calculate. https://we-calculate.com/ga/calculator/log-calculator
TG we-Calculate Editorial Team. "Logarithm Calculator — log₁₀, ln, log₂, Any Base." TG we-Calculate. 2026. https://we-calculate.com/ga/calculator/log-calculator.
TG we-Calculate Editorial Team, "Logarithm Calculator — log₁₀, ln, log₂, Any Base," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/ga/calculator/log-calculator
@misc{wecalculate_log_calculator, title = {Logarithm Calculator — log₁₀, ln, log₂, Any Base}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/ga/calculator/log-calculator}}, year = {2026}, note = {TG we-Calculate} }
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