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List of logarithmic identities
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== Approximating large numbers == The identities of logarithms can be used to approximate large numbers. Note that {{math|1=log<sub>''b''</sub>(''a'') + log<sub>''b''</sub>(''c'') = log<sub>''b''</sub>(''ac'')}}, where ''a'', ''b'', and ''c'' are arbitrary constants. Suppose that one wants to approximate the 44th [[Mersenne prime]], {{math|2<sup>32,582,657</sup> −1}}. To get the base-10 logarithm, we would multiply 32,582,657 by {{math|log<sub>10</sub>(2)}}, getting {{math|1=9,808,357.09543 = 9,808,357 + 0.09543}}. We can then get {{math|1=10<sup>9,808,357</sup> × 10<sup>0.09543</sup> β 1.25 × 10<sup>9,808,357</sup>}}. Similarly, [[factorial]]s can be approximated by summing the logarithms of the terms.
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