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Logarithm Calculator

Compute common log (log₁₀), natural log (ln), binary log (log₂), and a custom-base logarithm for any positive number.

Common Log (log₁₀)
2.0000
Natural Log (ln)
4.6052
Binary Log (log₂)
6.6439
Custom (log_10)
2.0000
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Calculation Guide & Reference

Logarithm Mathematics

Logarithm calculator computes common log (log₁₀), natural log (ln), binary log (log₂), and a custom-base log for any positive number.

Standardized Mathematical Formula
log_b(x) = y ⟺ b^y = x

A logarithm answers "to what power must the base be raised to get this number?" Common log uses base 10, natural log uses base e (≈2.71828), and binary log uses base 2.

Variables:
x:The argument (must be positive)
b:The base of the logarithm
How It Works (Step-by-Step)
  • 1Enter the number (argument) and, optionally, a custom base.
  • 2View the common log, natural log, binary log, and custom-base log.
Real-World Numerical Example
Logarithms of 100

Compute several logarithms of 100.

•Common log: log₁₀(100) = 2, since 10² = 100.
•Natural log: ln(100) ≈ 4.6052.
•Binary log: log₂(100) ≈ 6.6439.
Result: log₁₀(100) = 2, ln(100) ≈ 4.6052, and log₂(100) ≈ 6.6439.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

"log" (without a subscript, in most contexts) means log base 10, the common logarithm. "ln" specifically means the natural logarithm, base e (≈2.71828), which is the inverse of the exponential function eˣ.

Because no real exponent applied to a positive base ever produces a negative result or zero — the logarithm function is only defined for positive arguments in the real number system.

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