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logarithmsmore about logarithms

logarithms

 

  2  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Logarithm  \Log"a*rithm\  (l[o^]g"[.a]*r[i^][th]'m),  n.  [Gr. 
  lo`gos  word  account,  proportion  +  'ariqmo`s  number:  cf  F. 
  logarithme.]  (Math.) 
  One  of  a  class  of  auxiliary  numbers,  devised  by  John  Napier, 
  of  Merchiston  Scotland  (1550-1617),  to  abridge  arithmetical 
  calculations,  by  the  use  of  addition  and  subtraction  in  place 
  of  multiplication  and  division. 
 
  Note:  The  relation  of  logarithms  to  common  numbers  is  that  of 
  numbers  in  an  arithmetical  series  to  corresponding 
  numbers  in  a  geometrical  series,  so  that  sums  and 
  differences  of  the  former  indicate  respectively 
  products  and  quotients  of  the  latter;  thus  0  1  2  3  4 
  Indices  or  logarithms  1  10  100  1000  10,000  Numbers  in 
  geometrical  progression  Hence  the  logarithm  of  any 
  given  number  is  the  exponent  of  a  power  to  which 
  another  given  invariable  number,  called  the  base,  must 
  be  raised  in  order  to  produce  that  given  number.  Thus 
  let  10  be  the  base,  then  2  is  the  logarithm  of  100, 
  because  10^{2}  =  100,  and  3  is  the  logarithm  of  1,000, 
  because  10^{3}  =  1,000. 
 
  {Arithmetical  complement  of  a  logarithm},  the  difference 
  between  a  logarithm  and  the  number  ten 
 
  {Binary  logarithms}.  See  under  {Binary}. 
 
  {Common  logarithms},  or  {Brigg's  logarithms},  logarithms  of 
  which  the  base  is  10;  --  so  called  from  Henry  Briggs,  who 
  invented  them 
 
  {Gauss's  logarithms},  tables  of  logarithms  constructed  for 
  facilitating  the  operation  of  finding  the  logarithm  of  the 
  sum  of  difference  of  two  quantities  from  the  logarithms  of 
  the  quantities,  one  entry  of  those  tables  and  two 
  additions  or  subtractions  answering  the  purpose  of  three 
  entries  of  the  common  tables  and  one  addition  or 
  subtraction.  They  were  suggested  by  the  celebrated  German 
  mathematician  Karl  Friedrich  Gauss  (died  in  1855),  and  are 
  of  great  service  in  many  astronomical  computations. 
 
  {Hyperbolic,  or  Napierian},  {logarithms} 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Logistic  \Lo*gis"tic\,  Logistical  \Lo*gis"tic*al\,  a.  [Gr.  ? 
  skilled  in  calculating,  ?  to  calculate,  fr  lo`gos  word 
  number,  reckoning:  cf  F.  logistique.] 
  1.  Logical.  [Obs.]  --Berkeley. 
 
  2.  (Math.)  Sexagesimal,  or  made  on  the  scale  of  60;  as 
  logistic,  or  sexagesimal,  arithmetic. 
 
  {Logistic},  or  {Proportional},  {logarithms},  certain 
  logarithmic  numbers  used  to  shorten  the  calculation  of  the 
  fourth  term  of  a  proportion  of  which  one  of  the  terms  is  a 
  given  constant  quantity,  commonly  one  hour,  while  the 
  other  terms  are  expressed  in  minutes  and  seconds;  --  not 
  now  used




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