What does 'change of base' mean?

It's a way to compute a logarithm in any base using only natural log: log_b(x) = ln(x) ÷ ln(b), which is what this tool uses internally regardless of which base you pick.

What's the difference between log and ln?

"log" commonly means base-10 (common log) and "ln" means natural log (base e) — this tool lets you pick either explicitly, or a custom base.

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Math & Everyday

Log Calculator

Logarithm of any number in base 10, base e, base 2, or a custom base.

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About the Log Calculator

Computes the logarithm of a number in base 10 (common log), base e (natural log), base 2 (binary log), or any custom base you choose.

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How to use it

Enter x, the number to take the logarithm of.
Choose a base: common (10), natural (e), binary (2), or a custom base.
Read the result.

Formula

log_b(x) = ln(x) ÷ ln(b) (change of base formula), computed via natural log internally regardless of which base is selected.

Worked example

log base 2 of 8 = 3, since 2³ = 8. Log base 10 of 1000 = 3, since 10³ = 1000.

Recommendations

• Base 2 (binary log) is common in computer science.
• Natural log (base e) appears throughout calculus, compound growth, and exponential decay formulas.
• A logarithm undoes exponentiation: log_b(x) answers 'to what power must b be raised to get x?'

Frequently asked questions

No real power of a positive base produces zero or a negative result, so the logarithm is undefined there.