16 PRACTICAL MATHEMATICS 



10. In working with logarithms to the base 10, and logarithms 

 to the base e, many students find difficulty in changing from one 

 system to the other. 



Let y be the common logarithm and x the Napierian logarithm 

 of a certain number N. 



Then logio^ = y and N = 10" 



Also log e N = x and N = t? 



Hence 10" = e*. 



Taking common logarithms of both sides 

 y = x Iog 10 <? = 0-4343# 



N'cl'D lO(? 



Thus common log = 0-4343 Nap. log or ;', 



J-3026 



common log 



and Nap. log = & or 2-3026 common log. 



0-4o4o 



EXAMPLES I 



(1) Working correct to four significant figures, find the 

 factors of 



(a) x 2 + 3-94^ - 5-62 



(b) x 2 - 5-72x + 4-77 



(c) x 2 - 8-Q2x - 4-86 



Find the partial fractions of 



3x+ 5 x*-2 



' ' (x- 3)(x+ 4) * ' x 2 - 4 



V / (ft i OWQ/v, 0\ \ I 



(6) 



(2x + 3)(3x- 2) (5x - 3) (3 - x) 



x 2 - 3x+ T 5x 2 + 7x - 



(x- l)(x+ 2)(x- 3) v ' (2x+ l)(3.r- 2)(3x + 1) 



( 8 ) 7^2 n\/ , n\ ( 9 ) 



(x 2 - 9)(x +2) (3- 2x)(x + 8)(5 - 3x) 



%'? i Q>i 1 f> RT^ *7 



^ OLU ~T~ Ofc6 X^5 y- ^ v *5tt/ 



< 10 ' (. + 4)3 <"> (T^ 



3 -ai;+ 1 



(J-qV (to+8)S 



< 14 ' J^r W s^- s 



(16) 



i^+1 l " (x 3 +8)(x+2) 



