In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number \(x\) to the base \(b\) is the exponent to which \(b\) must be raised, to produce \(x\). For example, since \(1000 = 10^3\), the logarithm base \(10\) of \(1000\) is \(3\), or \(\log_{10}(1000) = 3\). The logarithm of \(x\) to base \(b\) is denoted as \(\log_b(x)\), or without parentheses, \(\log_bx\), or even without the explicit base, \(\log x\), when no confusion is possible, or when the base does not matter such as in big O notation [Big-O notation].

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## References

“Logarithm.” 2022.

*Wikipedia*, December. https://en.wikipedia.org/w/index.php?title=Logarithm&oldid=1126519828.