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The pH of a solution is defined as the negative logarithm of the concentration of H+, and the pOH is defined as the negative logarithm of the concentration of OH-. For example, the pH of a 0.01M solution of hydrochloric acid (HCl) is equal to 2 (pH = −log 10 (0.01)), while the pOH of a 0.01M solution of sodium hydroxide (NaOH) is equal to 2 ...
For example, if the concentration of the conjugate base is 10 times greater than the concentration of the acid, their ratio is 10:1, and consequently the pH is pK a + 1 or pK b + 1. Conversely, if a 10-fold excess of the acid occurs with respect to the base, the ratio is 1:10 and the pH is p K a − 1 or p K b − 1.
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Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table. [53]
Graph of the number of primes ending in 1, 3, 7, and 9 up to n for n < 10 000. Another example is the distribution of the last digit of prime numbers. Except for 2 and 5, all prime numbers end in 1, 3, 7, or 9. Dirichlet's theorem states that asymptotically, 25% of all primes end in each of these four digits.
This is an accepted version of this page This is the latest accepted revision, reviewed on 11 December 2024. Motorsport championship held worldwide "F1", "Formula 1", and "FIA World Championship" redirect here. For other uses, see F1 (disambiguation), Formula One (disambiguation), and List of FIA championships. Formula One Formula One logo since 2018 Category Open-wheel single-seater Formula ...
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The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...