This log calculator helps you calculate logarithms, solve for the original value, and solve for the base. It is based on the standard logarithm definition and the change-of-base formula, which lets any logarithm be evaluated as ln(x) / ln(b). For a trusted reference, see the NIST Handbook and standard logarithm definitions: NIST.
What this calculator does
The tool supports three main tasks:
- Find a logarithm: calculate y = logb(x)
- Find the original value: calculate x = by
- Find the base: solve for b when logb(x) = y
It also shows the change-of-base setup, rounded and more precise results, and a live graph below the inputs to help visualize how the logarithm behaves.
How to use it
- Choose the type of calculation.
- Enter the required values.
- Click Calculate.
- Read the result, formula breakdown, and explanation.
Important rules
For real logarithms, the argument must be greater than 0, the base must be greater than 0, and the base cannot equal 1. If the inputs break these rules, the calculator will show an error instead of an invalid result.
Why the graph helps
The graph shows how y = logb(x) changes based on your inputs. It makes it easier to see where the selected point sits on the curve and how the base affects the shape of the logarithm.
Where this is useful
This calculator is useful for algebra, precalculus, exam prep, homework, formulas involving logarithms, and quick checks in science, engineering, and data work.
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