Approximating Large Numbers
The identities of logarithms can be used to approximate large numbers. Note that logb(a) + logb(c) = logb(ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 232,582,657 − 1. To get the base-10 logarithm, we would multiply 32,582,657 by log10(2), getting 9,808,357.09543 = 9,808,357 + 0.09543. We can then get 109,808,357 × 100.09543 ≈ 1.25 × 109,808,357.
Similarly, factorials can be approximated by summing the logarithms of the terms.
Read more about this topic: List Of Logarithmic Identities
Famous quotes containing the words large and/or numbers:
“The old, subjective, stagnant, indolent and wretched life for woman has gone. She has as many resources as men, as many activities beckon her on. As large possibilities swell and inspire her heart.”
—Anna Julia Cooper (1859–1964)
“Our religion vulgarly stands on numbers of believers. Whenever the appeal is made—no matter how indirectly—to numbers, proclamation is then and there made, that religion is not. He that finds God a sweet, enveloping presence, who shall dare to come in?”
—Ralph Waldo Emerson (1803–1882)