Method
log_b(x) = ln(x) ÷ ln(b), meaning the exponent to which b must be raised to produce x.
Math worksheet
Logarithm Calculator
Evaluate a logarithm in any valid base and compare natural-log and common-log forms.
The calculation runs locally. Exact-integer tools avoid floating point; decimal and transcendental tools report rounding limits.
Method and verification guide
How the Logarithm Calculator works
log_b(x) = ln(x) ÷ ln(b), meaning the exponent to which b must be raised to produce x. The calculator keeps the intermediate values visible so you can reproduce the answer independently.
Interpret the result
The power check raises the base to the result and should return the original number.
Check the assumptions
For real logarithms, x must be positive and the base must be positive and not equal to 1.
Local calculation
Everything runs in this browser. Inputs are not sent to an external calculator.
Rounding
Displayed values may be rounded for readability while calculations use full floating-point precision unless the tool explicitly uses exact integers.
Scope
For real logarithms, x must be positive and the base must be positive and not equal to 1.
Simple by design
Three steps to a clearer number.
Enter your details
Use realistic values in each field. You can change them anytime.
Calculate instantly
The formula runs locally, so there is no account or waiting time.
Use the result
Treat the answer as a practical estimate for your next decision.