Free & Instant
Logarithm Calculator
Calculate the logarithm of any number with any base, instantly.
Logarithm Calculator
Calculate log values instantly.
Result (log)
0What is a Logarithm?
A logarithm answers the question "to what power must the base be raised to get this number?" For example, log base 10 of 100 is 2, since 10² = 100.
Logarithm Formula
log_b(x) = y, where b^y = x
Change of Base: log_b(x) = ln(x) / ln(b)
Frequently Asked Questions
What's the difference between log and ln?
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"log" typically refers to base-10 logarithm, while "ln" refers to the natural logarithm (base e, approximately 2.718). Enter base 10 or base e (2.71828) accordingly.
Can I take the logarithm of a negative number?
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No, logarithms of negative numbers or zero are undefined within real numbers, since no real exponent produces a negative or zero result from a positive base.
Where are logarithms commonly used?
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Logarithms are used in measuring earthquake magnitude (Richter scale), sound intensity (decibels), pH levels in chemistry, and exponential growth/decay calculations.