Logarithms. 199 



of .V be computed and tabulated, the results constitute a System of 

 Logarithms. 



Since an}- positive value except i may be chosen for the base 

 a, the number of different possible systems of logarithms is un- 

 limited. In fact, however, only two systems have ever been 

 tabulated ; the N'atural or Napcrian or Hyperbolic System, whose 

 base is approximately 2. 7 1828 18-}-, and the Common or Briggs' 

 System, whose base is 10. 



The Naperian logarithms of all numbers from i to 20,000 have 

 been computed to 27 places of decimals. The common logar- 

 ithms of all numbers from 1 to over 200,000 have been found. 

 They are usually printed to seven decimal places, but they have 

 been computed to many more. 



The great value of a table of logarithms is the immense amount 

 of labor which can be saved by its use in multiplication, division, 

 evolution, or involution of numbers, as will be explained here- 

 after. 



5. Exa:\iples. Write the following equations, using the log- 

 arithmic notation : 



Express the following, using the exponential notation : 

 ^5- l^g.7(i)= — -3333+ 19' logjo24=io. 



16. log^_4=. 602060 20. loge^'=i. 



77. log^^^ioooo=4. 2^- logi,d'^ = l}. 



iS. log^^.ooooi = — 5. 22. logo^ — B. 



6. PKOirERTiES OF Logarithms. Inasmuch as logarithms 

 are merely the exponents of a fixed base, the properties of logar- 



