Math
Logarithm Calculator
Evaluate logarithms quickly with support for log base 10, natural log (ln), and any custom base you specify.
Evaluate logs in base 10, e, or any custom base.
Change of base
log_b(a) = ln(a) ÷ ln(b)
The calculator uses the change-of-base identity to evaluate any base with high precision, showing both natural and base-10 equivalents.
How to use
- Enter the argument (a) you want the log of.
- Select base 10, e, or type a custom base.
- Read the logarithm value with up to eight decimal places and copy-friendly formatting.
Example
Input: Argument = 256, Base = 2
Output: log₂(256) = 8
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Logarithm Calculator: logarithm calculator, log base calculator, log base 2 calculator, change of base calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Logarithm Calculator: Computes logarithms in base 10, base e, or any custom base. It's built around logarithm, log base 10, natural log, so you can go from a raw question to a checked answer without switching tools.
The math behind it: The calculator uses the change-of-base identity to evaluate any base with high precision, showing both natural and base-10 equivalents. The core relationship is log_b(a) = ln(a) ÷ ln(b), shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter the argument (a) you want the log of. (2) Select base 10, e, or type a custom base. (3) Read the logarithm value with up to eight decimal places and copy-friendly formatting. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering Argument = 256, Base = 2 returns log₂(256) = 8. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Can I log negative numbers?
Real logarithms only accept positive arguments. The calculator flags invalid inputs if the argument or base is non-positive.
Does it show natural logs too?
Yes—the results panel includes both log₁₀ and ln so you can compare values instantly.
What formula does the Logarithm Calculator use?
The calculator uses the change-of-base identity to evaluate any base with high precision, showing both natural and base-10 equivalents.
How do I use the Logarithm Calculator?
Enter the argument (a) you want the log of. Select base 10, e, or type a custom base. Read the logarithm value with up to eight decimal places and copy-friendly formatting.