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 |
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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.