UnitCompiler
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Log (Logarithm) Calculator

Evaluate logarithms for any base using the change-of-base formula.

📘 View 4-Figure Log & Antilog Tables →

Logarithm Calculator —logb(x)

Solve common logarithm log₁₀, natural logarithm ln (logₑ), binary log₂, and arbitrary custom bases.

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Standard Bases:
log10(1000) = 3 ⟺ 103 = 1000
Calculated Valuey = logb(x)
3
log10(1000) = 3  ⟺  103 = 1000
Common Log (log₁₀)
3.0000
Natural Log (ln)
6.9077
Binary Log (log₂)
9.9658

📐 Fundamental Logarithm Identities & Laws

Change of Base Rule
logb(x) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b)

Allows computing arbitrary base logarithms using standard natural or base-10 functions.

Product Rule
logb(x · y) = logb(x) + logb(y)

The log of a product equals the sum of the individual logarithms.

Quotient Rule
logb(x / y) = logb(x) − logb(y)

The log of a ratio equals the numerator log minus denominator log.

Power Rule
logb(xn) = n · logb(x)

Exponents on the argument can be brought to the front as multipliers.