A free logarithm calculator for any base, with the check and the change of base formula worked out.
Work out a logarithm to any base, natural, common or binary, with the check.
Your numbers
Base 10 is the common log, e the natural log (ln), 2 the binary log. Pick Other for any base.
Your result
Fill in the fields above to see your result.
Embed this tool on your site
Paste the code into any page: WordPress, Webflow, Squarespace, Ghost or plain HTML. It's free with the credit under it, which links back to navid.me.
This free logarithm calculator works out a logarithm to any base: the common log (base 10), the natural log (ln) or the binary log (base 2), and any other.
It shows the check, the base raised to the answer, so you can see why it's right.
I built it because most phone calculators only have log and ln, and changing the base by hand is where answers go wrong.
Here's what a logarithm is, the change of base formula, and a worked example.
TL;DRKey takeaways
What is a logarithm calculator?
A logarithm calculator finds the power you'd raise a base to, to get a number.
It's the opposite of a power: if 2³ = 8, then log base 2 of 8 is 3.
How logarithms work
Every logarithm comes back to the natural log. NIST's Digital Library of Mathematical Functions gives the change of base formula: log base a of z = ln z ÷ ln a.
A worked example
Here's the example the calculator loads: log base 10 of 50.
ln 50 = 3.912 and ln 10 = 2.303, so 3.912 ÷ 2.303 = 1.699. Check: 10^1.699 = 50.
Mistakes to avoid
These are the slips that come up most.
- Taking the log of 0 or a negative number, which has no real answer
- Mixing up log (base 10) and ln (base e)
- Dividing the numbers instead of their logs when changing base
Who is the logarithm calculator for?
It's for students, scientists and anyone working with growth or decibels, and these tools help around it.
- Scientific calculator – for any expression
- Fraction calculator – for answers as fractions
- Statistics calculator – for a list of numbers
Find the power once, and the check tells you it's right.
Plan your money with your AI
Take your numbers further in
Logarithm Calculator FAQs
Questions about the logarithm calculator? Here's what to know.
A logarithm calculator finds the power a base is raised to, to get a number.
This free one works in any base and shows the check.
A logarithm is the power you raise a base to, to get a number.
log base 10 of 1,000 is 3, because 10³ = 1,000.
log usually means base 10, and ln means base e, the natural log.
Divide the natural logs: log base a of x = ln x ÷ ln a.
3, because 2³ = 8.
No power of a positive base ever makes 0, so there's no answer.
1, since e¹ = e.
Yes, it's free with no sign-up.
It runs in your browser, and your numbers stay on your device.
I did.
I'm Navid Moazzez, and I made the logarithm calculator as one of my free tools on navid.me.
More about me.
Navid Moazzez
AI business strategist & AI OS builder
Navid Moazzez helps creators and founders master AI and build their own AI Operating System (AI OS) to automate their business and life.
Navid.me is reader-supported. When you buy through links on this site, I may earn an affiliate commission. Learn more.
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