Logarithm Calculator

Calculate logarithms with any base. Get log base 10, natural log (ln), log base 2, and custom base logarithms instantly.

Value (x)

Base (b)

Tab to move between fields

log_b(x)

ln(x) — Natural Log4.60517

log₁₀(x)2

log₂(x)6.643856

Formulalog₍10₎(100) = 2

How to Use This Calculator

Enter the value you want to take the logarithm of in the Value field; it must be a positive number.
Set the Base (default 10 for common log, or enter 'e' equivalent ≈ 2.718 for natural log, or 2 for binary log).
The result is the exponent to which the base must be raised to equal the value: log_b(x) = y means b^y = x.
Log base 10 is used in scientific notation and decibels; natural log (ln) appears in growth models and calculus.
Log base 2 is fundamental in information theory and computer science (bits of entropy).
Value must be strictly greater than 0 and base must be positive and not equal to 1.

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