Acevedo algorithm
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The Acevedo's Algorithm is a method developed by José Acevedo Jiménez to calculate logarithms. It involves raising a number a to successive powers of the base b, while multiplying the exponents by the number system base B. If the resulting value is less than b, the logarithm of a can be expressed as the sum of the exponents divided by successive powers of B. The document provides an example of using the algorithm to calculate the logarithm of seven in base 10 to three decimal places.
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Acevedo algorithm
- 1. Acevedo’s Algorithm The Acevedo's Algorithm is named after José Acevedo Jiménez who developed it. This is expressed as follows: 𝐴1 = 𝑎 𝑏 𝑥0 𝐴2 = ( 𝑎 𝑏 𝑥0 ) 𝐵 𝑏 𝑥1 𝐴3 = ( ( 𝑎 𝑏 𝑥0 ) 𝐵 𝑏 𝑥1 ) 𝐵 𝑏 𝑥2 𝐴 𝑛+1 = (( ( ( 𝑎 𝑏 𝑥0 ) 𝐵 𝑏 𝑥1 ) 𝑏 𝑥2 ⋮ 𝐵 ) ⋰ ) 𝐵 𝑏 𝑥 𝑛
- 2. if 1 ≤ 𝐴 𝑛+1 < 𝑏 then log 𝑏 𝑎 = 𝑥0 + ∑ 𝑥𝑖 𝐵−𝑖 𝑛 𝑖=1 Where: 𝑎 ∈ ℝ ≥ 1. 𝐵 = number system base, 𝐵 > 1. 𝑏 = logarithm base. Original sequence of the algorithm developed by Acevedo to calculate logarithms.
- 3. Example: Calculate the logarithm of seven in base 10 with three decimal places. 𝑎 = 7, 𝑏 = 10, 𝐵 = 10 ( ( ( ( ( 7 100) 10 108 ) 10 104 ) 105 10 ) 10 100 ) 10 109 < 7 log 𝑎 ≈ 𝑥0 + 𝑥1 𝐵−1 + 𝑥2 𝐵−2 + 𝑥3 𝐵−3 + 𝑥4 𝐵−4 + 𝑥5 𝐵−5 log10 7 ≈ 0 + 8 101 + 4 102 + 5 103 + 0 104 + 9 105 log 7 ≈ 0.84509