Log Calculator
Enter a number and a base (10, e for natural log, 2, or any custom base) to calculate the logarithm instantly.
Result
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Enter a number and base to calculate.
How the Log formula works
Using the change-of-base formula:
log_base(number) = ln(number) / ln(base)
This lets any base be calculated using natural logarithms, which is how most calculators and programming languages compute logs internally.
Step-by-step calculation
- Take the natural logarithm of the number.
- Take the natural logarithm of the base.
- Divide the first by the second.
Worked example
log base 2 of 32: ln(32)/ln(2) = 3.4657/0.6931 = 5, confirming that 2⁵ = 32.
Frequently asked questions
What's the difference between log and ln?
'log' typically refers to base-10 logarithm (common logarithm), while 'ln' specifically means natural logarithm, which uses the mathematical constant e (≈2.71828) as its base.
Can you take the log of a negative number or zero?
No — logarithms are only defined for positive real numbers, since no real power of a positive base produces a negative result or zero.