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LnCalc
Enter a number — get ln, log₁₀, and log₂ with the change-of-base formula shown.
The natural logarithm ln(x) uses base e ≈ 2.71828, Euler's number. It arises naturally in continuous growth/decay: if something grows at 100% per year compounded continuously, it multiplies by e each year. ln(x) answers 'what continuous rate for how long gives factor x?'
Any logarithm can be converted: log_b(x) = ln(x)/ln(b). So log₁₀(x) = ln(x)/ln(10) and log₂(x) = ln(x)/ln(2). This is useful because most programming languages and calculators provide ln directly.
ln(x)
2.303
What you entered
Natural logarithm: ln(x)
ln(10)= 2.3026Common log: log₁₀(x) = ln(x) / ln(10)
2.3026 / 2.3026= 1Binary log: log₂(x) = ln(x) / ln(2)
2.3026 / 0.6931= 3.3219Result
ln(x): 2.303
The natural logarithm of 10 is 2.303. In other bases: log₁₀(10) = 1 and log₂(10) = 3.322.