Logaritmes
 

HEyooo

Kan iemand mij wat basisdingen
vertellen over logartimes.Over
wanneer je het gebruikt,en over
de formules enzo?!

Wel dooen hoooor!!
TNX!!

MASTerr

Logaritmes is recentelijk nog geweest
Logaritmes gebruik je in de eerste plaats om een macht te weten te komen:
2^x=8
²log8=x
x=3

²log8 spreek je uit als: de twee log van 8
Dit toets je in door op je rekenmachine: log 8/log 2 te doen.
log 8 is eigenlijk de 10 log van 8. Maar die 10 laat je dan dus weg.

hmmm...ik was dus op 1 op andere manier uitgelogd terwijl ik dit postte.

Zie voor een historische bespreking over de gewone of Briggse logaritme (met grondtal 10) en de natuurlijke logaritme (ln, afgeleid van logaritmus naturalis met grondtal e) mijn replies hierover in http://forum.scholieren.com/showthre...ight=logaritme

Laten we het Napier zelf vragen. In Mirifici logarithmorum canonis descriptio (1614) schrijft hij:

Seeing there is nothing (right well-beloved Students of the Mathematics) that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are for the most part subject to many slippery errors, I began therefore to consider in my mind by what certain and ready art I might remove those hindrances.
And having thought upon many things to this purpose, I found at length some excellent brief rules to be treated of (perhaps) hereafter. But amongst all, none more profitable than this which together with the hard and tedious multiplications, divisions, and extractions of roots, doth also cast away from the work itself even the very numbers themselves that are to be multiplied, divided and resolved into roots, and putteth other numbers in their place which perform as much as they can do, only by addition and subtraction, division by two or division by three.

Als je dit goed leest staat er dat hij graag af wilde van al die lastige vermenigvuldigingen, die delingen en dat worteltrekken. Logaritmen waren in eerste bedoeld om berekeningen te versnellen.


The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculatory science with his discovery of logarithms.

http://www-groups.dcs.st-and.ac.uk/~...ns/Napier.html

http://www-groups.dcs.st-and.ac.uk/~...ns/Briggs.html


alog b = c <=> ac = b Voorwaarden:a>0 en a¹1 en c>0
^5log 125 = 3 , want 5^3 = 125

^alog 1 = 0 (want a° = 1)
^alog a = 1 (want a¹ = a)

^alog b = log b/log a
^5log 12 = log 12/log 5 = 1,54

^alog bp = p.^alog b
^5log 4^3 = 3.^5log 4 = 3. log 4/log 5 = 3.0,861 = 2,58