Online Calculator

Logarithm
Calculator

Compute log₍b₎(x) with precision. Instant results, calculation history, and shareable links.

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What is a Logarithm?

A logarithm answers: "To what power must base b be raised to get x?"

If log₍b₎(x) = y, then bʸ = x

Base 10 — log₁₀(x)

Base e ≈ 2.718 — ln(x)

Base 2 — log₂(x)

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

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

Quotient: log₍b₎(x/y) = log₍b₎(x) − log₍b₎(y)

Power: log₍b₎(xⁿ) = n · log₍b₎(x)

Identity: log₍b₎(b) = 1

Zero: log₍b₎(1) = 0