Logarithm Base Calculator

Calculate logarithms with any valid positive base other than 1 and view the equivalent exponential form.

Domain rules: x > 0, base > 0, and base ≠ 1.

Result will appear here.
Metric Value

Privacy: calculations run locally in your browser. No values are stored or transmitted.

How it works

Formula:
logᵦ(x) = ln(x) / ln(b)
Equivalent meaning:
bʸ = x where y = logᵦ(x)

Examples

  • log₂(8) = 3
  • log₁₀(1000) = 3
  • log₃(9) = 2

FAQ

  • What does log base b of x mean?

    It asks what exponent y makes b^y = x. That exponent y is the logarithm value.

  • Why must x be positive?

    Real logarithms are defined only for positive arguments x.

  • Why can’t the base be 1 or negative?

    For real logarithms, the base must be positive and not equal to 1.

  • Are calculations stored?

    No. Everything runs locally in your browser.

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