202 Algebra. 



12. Examples. In these examples and in all the following 

 pages the Common Logajithin is designated by the symbol log 

 instead of log^^. Hence when no subscript appears we are to un- 

 derstand that the base is lo. 



1. log (1888 X 476^i492)=log i8884-log 476— log 1492. 



2. log [V789Xjt|-|)5]=ilog 789 + 5 log 239-5 log 930. 

 fv/2 ^5 



'^^' ' Vxo 



= what? 



4.. log/,(<:V<?-7-/X'w)=what? 

 5. logz;(/2^^^^^^) = what? 



7- log/>^^^=what? 



cV. log/; ^^^= what? 

 9. Prove loga(logb^^') = loga^. 

 I 



10. Prove log^i^: 



loge«' 



13. Characteristic and Mantissa. For reasons which will 

 appear later the common logarithm of a number is always writ- 

 ten so that it shall consist of a positive decimal part less than i 

 and an integral part which may be either positive or negative. 

 Thus the common logarithm of .0256 is really —i. 591 76, since 



io-»"»=-^-^,'„,,= .b256. 



59176 



But instead of writing 



log.o256= — 1.59176 

 we write the equivalent equation 



log .0256= — 2 -f. 40824, 

 or, as is the universal custom, with the minus sign over the 2, 

 log .0256=2.40824 

 The minus sign over the 2 shows that 2 is alone affected ; that 

 is, the decimal fraction following it is positive. The student must 

 always take especial cat e to correctly hiterpret this method 0/ notatio?i. 

 When the logarithm of a number is arranged so that it consists 

 of a positive decimal part less than i and an integral part either 



