Logarithm Calculator

Compute log₍b₎(x) — instant, precise, and shareable.

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What is a Logarithm?

A logarithm answers: "To what power must base b be raised to get x?"
log₍b₎(x) = y means bʸ = x.

Change of Base: log₍b₎(x) = ln(x) / ln(b)

Product rule: log₍b₎(xy) = log₍b₎(x) + log₍b₎(y)

Quotient rule: log₍b₎(x/y) = log₍b₎(x) - log₍b₎(y)

Power rule: log₍b₎(xʸ) = y·log₍b₎(x)

Root rule: log₍b₎(ⁿ√x) = log₍b₎(x) / n

Base reciprocal: log₍b₎(x) = 1 / log₍x₎(b)

Identity: log₍b₎(b) = 1

Zero property: log₍b₎(1) = 0

Inverse property: b^(log₍b₎(x)) = x

log₁₀(1000) = 3 because 10³ = 1000.

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