About this calculator
Logarithm Calculator is a practical maths tool for students, teachers, spreadsheet users, and anyone checking a calculation quickly. Use it to calculate common logs, natural logs, base 2 logs, custom-base logs, and antilogs. It is designed to show both the result and the method, so the page is useful for learning, revision, homework checking, and everyday calculations.
Logarithm Calculator formula and method
The calculator uses the change-of-base formula, dividing the natural log of the number by the natural log of the base.
- log_b(x) = ln(x) / ln(b)
- ln(x) = log_e(x)
- antilog_b(y) = b^y
How to use the Logarithm Calculator
- Enter the main number, expression, equation, or parameters requested by the calculator.
- Check signs, brackets, powers, roots, and decimal points before calculating.
- Review the highlighted result first, then read the supporting working or notes.
- Change one input at a time if you want to compare examples or test your understanding.
- Keep exact values where possible and round only at the final step.
- Use the related calculators when the problem needs a second step, such as rounding or factorisation.
Worked examples
Common log
Input: log base 10 of 100
Calculation: 10 raised to 2 equals 100.
Result: log10(100) = 2.
Custom base
Input: log base 2 of 32
Calculation: 2 raised to 5 equals 32.
Result: log2(32) = 5.
Log laws
| Law | Meaning |
|---|---|
| log(ab) | log(a) + log(b) |
| log(a/b) | log(a) - log(b) |
| log(a^n) | n log(a) |
Valid inputs
The number must be positive, and the base must be positive and not equal to 1.
Common mistakes to avoid
- Mistake 1
- Do not take a real logarithm of zero or a negative number.
- Mistake 2
- Do not use base 1.
- Mistake 3
- Remember that ln means base e, not base 10.
Edge cases
- Some expressions are undefined, such as division by zero or logarithms of non-positive numbers.
- Different courses may prefer exact radical form, decimal form, interval notation, or a specific rounding rule.
- Very large integer results can become hard to read even when the arithmetic is correct.
- Typed expression parsing supports common notation, but unusual algebra layouts may need rewriting.
Limitations
This calculator is for general educational information only. It follows standard school-level and early college-level maths conventions, but it cannot replace your course instructions, teacher feedback, or specialist software for formal work.
- Check whether your answer should be exact, rounded, simplified, or written in a particular notation.
- Expression and equation parsers are intentionally simple and may not understand every possible layout.
- For high-stakes technical or engineering calculations, verify the result independently.
Frequently asked questions
Can I use decimals?
Yes, most calculators in this batch accept decimal inputs where decimals make sense.
Why does notation matter?
The same mathematical idea can be written in several ways, but calculators need a clear typed format.
Should I round intermediate steps?
Usually no. Keep full precision until the final answer unless instructed otherwise.
Are these calculators suitable for GCSE revision?
Many are useful for GCSE and A-level style practice, especially BODMAS, inequalities, roots, sequences, and simultaneous equations.
What if my answer looks different from a textbook?
It may be equivalent in another form. Check by substituting values or simplifying both forms.
Related calculators
- Exponent and Root Calculator
- Scientific Calculator
- Scientific Notation Calculator