Logarithm Calculator
Log undoes exponentiation — this answers 'what power do I raise the base to, to get this value?' in any base, not just the common base-10 and natural-log versions a basic calculator offers.
Inputs
Result
3
ln = 6.907755 · log₁₀ = 3
How the logarithm calculator works
log_base(value) = ln(value) ÷ ln(base), using the change-of-base formula, since most underlying math libraries only implement natural log directly.
The natural log (ln) and base-10 log (log₁₀) are shown alongside the requested base as a quick cross-reference.
Worked example: log base 10 of 1000
- ln(1000) ≈ 6.9078, ln(10) ≈ 2.3026.
- log₁₀(1000) = 6.9078 ÷ 2.3026 = 3.
- Check: 10³ = 1000, confirming the log is exactly 3.
Common mistakes to avoid
Trying to take the log of zero or a negative number
Logarithms are only defined for positive real numbers — there is no real exponent that produces zero or a negative result from a positive base.
Assuming log always means base 10
In many math and science contexts, especially calculus and computing, 'log' silently means natural log (base e) or base 2. Always confirm which base a problem intends before comparing answers.
Frequently asked questions
What is the natural log (ln) actually used for?
It's the log with base e ≈ 2.71828, and it appears throughout calculus, compound growth, and any process involving continuous (rather than stepped) change.
Why is log base 2 relevant in computing?
It answers 'how many times can this be halved (or doubled)?', which is exactly the question behind binary representations, algorithm complexity, and data-size doubling.
How do I undo a logarithm to get back the original value?
Raise the base to the power of the log result — if log_b(x) = y, then b^y = x exactly.
Can this compute a log with a fractional or unusual base, like base 0.5?
Yes, the change-of-base formula works for any valid base greater than 0 and not equal to 1.
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