Example : To find tt^, given 



In 7r= 1.14472,98858,49400,17414,34273 

 Solution : 



In TT^ = 2.28945,97716,98800,34828,685 

 In 10^ = 6.90775,52789,82137,05205,397 (plus) 



9. 19721 ,50506,80937,40034,082 

 In"^ 9.19715,38101.72007,17851,824 = 9869 



6,12405,08930,22182,258 

 In-i 6, 1 1981 ,27356,40346,909 = 1 .0^0612 



423,81573,81835,349 

 In-i 423,79999,10196,783= 1.0'4238 



In-^ 0. 0^ , 0' ,01574,71638,566=1.0^4574 . . . , 



the fourth factor of the desired number. Since 0.0^U574 ... is the In of a 

 number of the form /n(lH-jr), we have from the equivalent series: 



x-xV2 = 0.0in574,71638,566 



x=0.0in574,71638,566 + A-V2 



= 0.0^4574,71638,566+0.0-423 

 x = 0.0^4 574,71638,566 



Hence /n-i(0.0"1574,71638,566) = 1.0"1574,71638,566. Thus 7r-=(9869) 

 (1.0^0612) (1.0H238) (1.0^4574,71638,566) (10-«) =9.86960,440 10,893 58,- 

 61883,44 in which there is an error of one unit in the last decimal place. 



Instead of commencing by deducting In 9869 it would be just as con- 

 venient to deduct In 9868 or any logarithm down to In 9860, and then proceed, 

 as before, to the use of table 1. In general any number whose logarithm, 

 when subtracted from the given logarithm, results in a remainder that falls 

 within the tabular values found in the second column of table 1 may be used. 



In finding an antilogarithm when the common logarithm of a number is 

 given, the procedure is much the same as that when the natural logarithm is 

 given. When selecting the initial log nearest the value of the given log, it is 

 advisable to select the log found between the tabular values for the numbers 

 1,000 to 10,000. 



The only significant difference when working with the common logarithms 

 of table 2 is found in the computed value of the log of the fourth factor, 

 l.O^^XXXX. . . . The following example will readily explain the procedure 

 to follow : 



Example : To find e, given 



log 6 = 0.43429,44819,03251,82765,1 13 



log-^ 0.43408,96384,17890,77149,304=2.717 



' 20,48434,85361,05615.809 

 log-^ 20,48084,06847,61790,274= 1.0H717 



350,78513,43825,535 

 log-i 350,77963,88670,210= 1.0^8077 



log-' 0.0^ , 0" ,00549,55 155,325 may be found by the same 



