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Logarithm Calculator
Compute the logarithm of any positive number in any base, with the change of base formula worked out for you.
HOW TO USE
- 1Enter the number x you want the logarithm of, it must be greater than 0.
- 2Enter the base b. It must be greater than 0 and cannot be 1, with base 1 every logarithm would be undefined.
- 3The result shows the answer plus the change of base formula: logᵦ(x) = ln(x) / ln(b), with the actual values substituted.
- 4Base 10 (common) and base e (natural) are the most common, the change of base formula converts any other base to them.
EXAMPLE
INPUT
x = 100, base = 10
OUTPUT
log₁₀(100) = ln(100) / ln(10) = 4.60517 / 2.302585 = 2
FAQ
What is the change of base formula?
It is logᵦ(x) = ln(x) / ln(b), and the natural logarithm can be replaced by any base you like. It lets you evaluate logarithms in any base using a single function.
Why must the number be greater than 0?
The logarithm asks which exponent of the base gives the number. Since a positive base raised to any real exponent is always positive, only positive numbers have real logarithms.
Why is base 1 not allowed?
1 raised to any exponent is 1, so no exponent produces any other value. The formula also divides by ln(1) = 0, which is undefined.
What are common and natural logarithms?
The common logarithm uses base 10 (written log₁₀ or just log), and the natural logarithm uses base e ≈ 2.71828 (written ln). Both are special cases of the same formula.
Is my data sent anywhere?
No. All calculations run entirely in your browser, your numbers never leave your device.