The identities of logarithms can be used to approximate large numbers. Note that log("a") + log("c") = log("ac"), where "a", "b", and "c" are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 − 1. To get the base-10 logarithm, we would multiply 32,582,657 by log(2), getting 9,808,357.09543 = 9,808,357 + 0.09543. We can then get 10 × 10 ≈ 1.25 × 10.

Similarly, factorials can be approximated by summing the logarithms of the terms.

स्वयंस्पष्ट सर्वसमिकाएँ (Trivial identities)
बड़ी संख्याओं का सन्निकटीकरण (Approximating large numbers)
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