Example1 Calculate log logylogs25

Solution Simplifyfromtheinsideout109311094 logs25 I 1093logy21 logsE

sincelogs1251 logs57 2time

logo2 logy4 IzNowlogz t is inexactform soleaveitlikethat Ba

Example2 Solvefor e210979 2 z o

Solution Firstbringthe 1 totheotherside thentakeInofbothsidese2

109717 2 1Infe2 109717

2In1

2 log717 2 O sinceIhle l Bo2 t x12 O de sincelogy7g Ed

X 4 Bk

Example3 Findthedomainof fix In 1 IncexDSolution Forthis youhavetoknowthatthedomainof In is o x becausetherangeofexiscordSinceAxlhastwoh's therearetworestrictionsinitsdomain

fix _In 1 Ink 2

IoThuswegettworestrictions e I 0 and 1 Ince x'I o Let'ssimplify these

e I o 1 Incex4 Oe X I Ince Xen txt e e x a applyexpbasee tobothsidesrecycler x2 o

x10Therefore thedomain istheintersectionof and xelR reexere xto firere 403 D8

Example4 Calculatethelimitfiefarctan India

Solution Youknow 4In11 0 Ifwereplace xby11 thisallowsustotakethelimitofIn11fromeithersideof o youget himInCixi x

Xsosincearctanlx s E as x o weget

hIyoarctanIndia arctan LingoInk E Ba

Exampies Letfat e Find f111Solution If x f 111 thenfall 1 Thuswehavetosolve

ex ex2

1

Let'sdoit ex e 2e t I 2e a multiplybothsidesbyex noting e e e

e 2e 1 0 andexe 1

Thisissecretly a quadraticequationinthevariable y e

y 2y I O

fit o fe xie