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Calculate log base 10, natural log (ln), log base 2, and logarithm of any custom base.
Logarithm Formulas:
log10(x): common logarithm (base 10)
ln(x): natural logarithm (base e = 2.71828...)
log2(x): binary logarithm (base 2)
Change of base: log_b(x) = ln(x) / ln(b)
Inverse: if log_b(x) = y, then b^y = x
A logarithm answers the question: to what power must the base be raised to get a certain value? For example, log10(1000) = 3 because 10^3 = 1000.
The natural logarithm uses Euler's number e (≈ 2.71828) as its base. It appears naturally in calculus, exponential growth/decay, and many scientific formulas.
Log base 2 (binary logarithm) tells you how many times you can halve a number before reaching 1. It is widely used in computer science to measure information and algorithm complexity.
The change-of-base formula lets you compute any logarithm using any available log function: log_b(x) = log(x) / log(b) = ln(x) / ln(b).
Logarithms are only defined for positive real numbers. There is no real power to which any base can be raised to produce zero or a negative number.