2o8 Algebra. 



logarithms lie between .4082400 and .4166239 are on the speci- 

 men page we give. Suppose, as an example, that we wish to 

 find the number corresponding to the logarithm 2.4127469. The 

 characteristic 'merely affects the decimal point, and consequently 

 the problem is merely to find the significant figures which cor- 

 respond to the given mantissa. The nearest mantissa printed in 

 the table is .4127461 and this corresponds to the figures 25867. 

 Hence, pointing off the number by means of the characteristic, we 

 find that the number whose logarithm is 2.4127469 is 258.67. 

 In connection with tables of logarithms methods are explained by 

 means of which more figures of this number could be found by 

 means of tables of multiples and differences, or of proportional parts. 



22. Examples. 



1. Find the logarithm of 25734. 



2. Find the logarithm of 26000000. 

 J. Find the logarithm of 25.999 



/. Find the logarithm of .02578411 



5. Find the logarithm of .260099 



6. Find the number whose logarithm is 3.4147561 



7. Find the number whose logarithm is 0.4104400 



8. Find the number whose logarithm is 2.415999 



9. Find the number whose logarithm is 1.4094094 

 10. Find the number whose logarithm is 7.4100000 



23. Multiplication by Logarithms. Formula {a) (Art. 7) 

 enables us to find the product of several numbers by means of a 

 table of logarithms. Thus, suppose we wish the product of 9.S 

 by 265. From a table of logarithms we find 



log 98= 1.9912261 



log 265= 2.4232459 



log 98 X 265=4.4144720 



From the table of logarithms (see sample page) it is found that 



4.4144720 is the logarithm of 25970. Therefore 98 X 265 = 25970. 



