Log Calculator — Logarithm of Any Base
Find the logarithm of a number in any base. A logarithm answers: to what power must the base be raised to get this number?
Updated
Formula
log_b(x) = y ⇔ bʸ = x
log_b(x) = ln(x) ÷ ln(b)
The second line is the change-of-base formula, used to compute logs in any base.
Examples
log₁₀(1000)
log10(1,000) = 3
ln(20)
ln(20) = 2.9957322736
log₂(1024)
log2(1,024) = 10
Important information
- Logs turn multiplication into addition, which is why they appear in pH, decibels, Richter scale earthquake sizes and compound-interest time calculations.
Frequently asked questions
What is ln?
The natural logarithm — log base e, where e ≈ 2.71828.
Can I take the log of zero or a negative number?
No. Logarithms are only defined for positive numbers.
How long to double money at 12%?
ln(2) ÷ ln(1.12) ≈ 6.1 years.
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