Log Calculator — One or 100 Values with Steps
Enter one positive value for a quick answer, or paste a column to calculate every row with the same base.
One value stays simple; a pasted column keeps its rows
Use the first line exactly like an ordinary log calculator. If a worksheet has several x values for the same base, paste up to 100 non-empty lines. A zero, negative, expression, overflow, or underflow is marked on its physical line without removing valid calculations.
Actual change-of-base steps for each input
Every valid result shows log_b(x) = ln(x) / ln(b), substitutes the browser's working values, then separates the working approximation from the result shown to your selected 2–12 decimal places.
The power check measures display rounding
Raising the base to the final displayed y shows how much the chosen decimal-place setting changes the reconstructed x. This is a display-precision check—not an independent verification and not an arbitrary-precision calculation. If the power becomes zero or infinite in browser floating-point arithmetic, the check is reported as unavailable.
Real-number scope
This calculator accepts finite positive x values and a finite positive base other than one. It supports base 2, base 10, e, or another valid real base. It does not solve logarithmic equations, simplify symbolic expressions, or calculate complex logarithms.
Frequently asked questions
How do you calculate a logarithm with any base?
For a valid real base b and positive x, use the change-of-base formula log_b(x) = ln(x) / ln(b). This page substitutes the browser's working approximations into that formula for every input row.
What values are allowed in a real logarithm?
The value x must be greater than zero. The base must be greater than zero and cannot equal one. This calculator does not evaluate complex logarithms or symbolic expressions.
Can I calculate log base 2, log base 10, or natural log?
Yes. Use the 2, 10, or e preset, or enter another valid positive real base. The same base is applied to every value in the current batch.
Are the displayed logarithms exact?
No. Irrational logarithms generally do not have finite decimal representations, and browser Math.log uses floating-point arithmetic. Results and substituted values are labeled working approximations.
What does the displayed-value precision check mean?
It raises the selected base to the final displayed logarithm and compares that value with x. It demonstrates the effect of display rounding; it is not an independent proof of accuracy. Overflow or underflow is shown as unavailable.
Can I calculate multiple logarithms at once?
Yes. Paste up to 100 positive values, one per line. Valid rows keep their physical line numbers, invalid real-domain inputs stay visible, and the results can be copied as a tab-separated table.