LOG 



6. "If <,p} be the perpendicular dropped from a given point (A", v%) o 

 the straight line y a x 4- b ; then 



- . -- 



va-f 8 ; * 



LITUUS. See Spiral. 

 LOGARITHMS. 



1. Properties of Logarithms. 

 Log. aXb Log. a -f. Log. fc. 



Log. y = Log. a Log. 6. 



Log. a l =. m Log. a. 

 | 



> 1 x 

 Log. a = - Log. . 



Log. a = Log. -. 



2 20 X 3^ X 2 031 

 Ex. I. Log. - 17 x 935Q J - = 20 lo 8T- 2 + 7 log. 3 + log. 2.013 



(log. 17 + log. 9350). 



8 x 2. Log. 5V 1<2 X ^ 51 3 ~ - = -jr (2 log. 317 -f * log. 3 + * 

 log. 5 log. 251). 



2. Given a number, to find its Logarithm. 

 Let 1 + x be the number, -m the modulus, 



then log. 1 + x = m ( x - ~ + |* - ? + & c .) 

 and log. 1 -JT = m X ( - A- - ^ - ^ - f. 4 - & c .) 

 ^^ = 2 W x( * + f + + & c .) 



Or since N = ^^y we may for x substitute ^[ p and we 



hall have 



