How to Use the Logarithm & Natural Log (ln) Calculator
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1
Enter your positive value $x$ (e.g. 100 or 256).
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The calculator computes: Common $\log_{10}(x)$, Natural Logarithm $\ln(x)$ (base $e \approx 2.71828$), and Binary $\log_2(x)$.
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3
Enter an arbitrary custom base $b$ (e.g. $\log_3(81)$).
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4
Review logarithmic identity expansions like $\log(ab) = \log a + \log b$.
Practical Example & Use Case
Common Real-World Scenario
Calculating $\log_2(1024) = 10$, confirming that $2^{10} = 1024$ in computer memory addressing.
Technical Notes & Limitations
Browser Engine Architecture
Logarithms are only defined for positive real numbers ($x > 0$) with base $b > 0$ and $b \ne 1$.
Frequently Asked Questions
What is the change of base formula?
$\log_b(x) = \frac{\ln(x)}{\ln(b)} = \frac{\log_{10}(x)}{\log_{10}(b)}$.