Log Calculator
Free online Log Calculator.
Calculator
How to Use
- Enter the required values
- Click Calculate to see the result
- Review the detailed output
Formula
log_b(x) = y means b^y = x. Common log (base 10). Natural log (base e). Change of base: log_b(x) = ln(x)/ln(b). Properties: log(ab) = log(a)+log(b).
Example Calculations
Common Log
Input: log base 10 of 10000
Result: 4 (because 10^4 = 10000)
Natural Log
Input: ln(e^3)
Result: 3 (because e^3 = e^3)
Custom Base
Input: log base 2 of 256
Result: 8 (because 2^8 = 256)
About This Calculator
Free online log calculator. Calculate instantly in your browser with our easy-to-use tool. No sign-up required.
Our log calculator is free, easy to use, and provides instant results. All calculations are performed in your browser for privacy and speed.
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Frequently Asked Questions
What is a logarithm?
Inverse of exponentiation. log base 10 of 1000 = 3, because 10^3 = 1000.
Natural log vs common log?
Common (log): base 10. Natural (ln): base e (~2.718). Natural in calculus, common in decibels/pH.
Log properties?
log(ab) = log(a)+log(b). log(a/b) = log(a)-log(b). log(a^n) = n*log(a).
Why no negative arguments?
b^x is always positive for real x, so no real x gives b^x = negative number.
Real-world uses?
Sound (decibels), earthquakes (Richter), acidity (pH), information theory, compound interest.