Logarithm Calculator
Calculate logarithms with any base, plus ln, log₁₀ and log₂. Free, fast and easy to use.
Enter a positive number x and a base b to calculate the logarithm log_b(x) – the power to which b must be raised to get x. The calculator also shows the natural logarithm (ln), the common logarithm (log₁₀) and the binary logarithm (log₂).
Formula
log_b(x) = y ⇔ bʸ = x log_b(x) = ln(x) / ln(b)
Calculations run locally in your browser. Results are for information only — for engineering, electrical or financial decisions, verify the assumptions and applicable standards.
- Number (x): 8 · Base (b): 2 → Logarithm log_b(x): 3
- Number (x): 81 · Base (b): 3 → Logarithm log_b(x): 4
- Number (x): 50 · Base (b): 10 → Logarithm log_b(x): 1,6989700043
- Number (x): 2,718281828 · Base (b): 2,718281828 → Logarithm log_b(x): 1
What is a logarithm?
The logarithm answers the question “to which power must the base be raised to get the number?”. log₂(8) = 3 because 2³ = 8, and log₁₀(1000) = 3 because 10³ = 1000.
How do I calculate a logarithm with a different base?
Use the change of base formula: log_b(x) = ln(x) / ln(b). For example, log₃(81) = ln 81 / ln 3 = 4.
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