TT8E OF THE TABLES.] 



MATHEMATICS. ALGEBRA. 



62: 



number, find the logarithm and subtract it from 10, in 

 the manner already explained. 



e. g. Find ar. comp. of log. 46-028. 



log. 46 028 = 1-6630221. 



ar. . comp. log. 46-028 = 8-3369778. 



(6). To find the product of several numbers by means of 



a Table of Logarithms. 

 We have seen that if N = xyz .... Then 



log. N = log. x -f log. y + log. z +, <fec 



Hence, find the logarithm of each number, add then: 

 together this gives the logarithm of the quotient find 

 the number corresponding to this logarithm, and we have 

 the product itself. 



Ex. Find the product of 52731 X 6 '0032 X '0759 

 log. 52-731 = 1-7220660 

 log. 6-0032 = -7783828 

 log. -0759 = 8- 8802418 10. 



24-026 



1-380C906 

 3806815 



91 

 91 





24-0265 Ans. 

 N.B. In any example of this kind, never use a 

 negative characteristic, such as 2-8802418. but 8-8802418 

 10 as above ; by doing so, there is nothing but straight- 

 forward addition to be performed until the end, when 

 ID can be easily struck off the characteristic of the sum. 



(7). To divide one number by another by means of a Table 

 of Logarithms. 



We have seen that if N . '. log. N -= log. log. y. 



. . log. N = log. x+ 10 log. y 10 



. . log. N = log. x -4- Ar. Comp. log. y 10. 



Hence, "To log. of numerator, add ar. comp. logarithm 

 of denominator, and subtract 10 from the sum this 

 gives logarithm of quotient. Find the number corres- 

 ponding to this logarithm, and the number is the quotient 

 required." 



Ex. Divide 37-052 by C741-6. 



log. 37-052 = 1-5C88U7 



Ar. : C. : log. G741-6 10 = 6-1712370 10 



540CO 



37400487 

 7400647 



20 

 16 



4 

 4,0 



005496025 Ans. 



(8) Similarly, if N = . We have- 

 log. N = log. o + log. 6 + log. c + Ar. C. log. x 10 



+ Ar. C. log. v 10 + Ar. C. log. z 10. 

 By this means log. N is found by a single addition 



.urn. Thus, find the value of JW2 X <*OM 



002 X 8746 5 X 3 124 

 4909693 



log. 3 0972 



log. 56-035 



Ar. C. log. -002 10 

 Ar. C. log. 8746 5 10 

 Ar. C. log. 3 124 10 



317153 



02 

 3-175802 Ans. 



1-748594. 

 12 6989700 10 

 6-0581667 10 

 9 5052890 10 



5018534 

 5018531 



3 

 2,7 



(9). To find any power of a, Number, we ham seen that if 



N = a" log. N = n log. a. 



Hence, if we multiply log. of the number by the index, 

 we obtain the logarithm of the power of the given 

 number ; and finding the number corresponding, we 

 obtain the power itself. 



Thus, find the fifth power of 2 00573 



20057 -3022660 



3 65 



log. 2 00573 

 Multiply by index 



32461 

 04 



3022725 

 5 



1-5113625 

 5113019 



32-46104 Ans. 



Again, fiud the third power of -02751. 

 log. -02751 



6 

 5,4 



8-4394906 10 

 3 



25 3184718 30 

 or, 5 3184718. 



We may in practice write this as as follows : 

 log. -02751 8 4394906 10 



3 



20819 



5 3184718 

 3184599 



119 

 104 



15 

 14,6 



A 113. 



IfN 



00002081957 

 (10). To find the Hoot of any Number. 



= a", then, 



log. N = - . log. a 



n 



Hence, " Find the logarithm of the given number ; 

 divide it by the number indicating the root this is the 

 logarithm of the required root the corresponding 

 number is the root itself " 

 Thus, extract the 5th root of 72 095. 



log. 72-095 5)1-8979051 



3795810 

 3795774 



36 

 2 36 



2-39652 Ans. 

 Again : extract the 7th root of -00972. 



Log -00972 = 3 -9876663 = 7-9876663 10. 

 All this has to be divided by 7- This will be effected 

 most easily by adding and subtracting such a multiple of 

 10 as shall make the negative part 70. 



te take log. -00972 = 67 9876663 70. 

 7)67-9876663 70 



31583 



05 



97125238 10. 

 7125234 



4 

 4.2 



5158505. Ans. 



If we had to extract the 6th root of the above number, 

 wo must of course take log. -00972 = 57 9876663 liO. 

 And again, to extract the cube root, we must take log. 

 00972 = 87 9876663 30. 



(11). The student must exercise himself in working 

 several examples, like each of those above given. Whou 



