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Chapter 4: Q. 78 (page 402)

Proveea+b=ea+ebforanyrealnumbera,b

Short Answer

Expert verified

ea+b=ea+ebforanyrealnumbera,bProved

Step by step solution

01

Step 1. To prove

ea+b=ea+ebforanyrealnumbera,b.

02

Step 2.  Solving LHS

Let,y=ea+bThen,y=ea+bIny=ln(ea+b)[TakingInonbothsides]Iny=a+bln(e1)=1Therefore,Iny=a+b.

03

Step 3.  RHS

Let,z=eaetThen,z=eaebln(z)=ln(eaeb)[TakingInonbothsides]lln(z)=ln(ea)+lneb[propertyoflogarithm]ln(z)=a+b[ln(e1)=1]Therefore,Inz=a+b.

04

Step 4. Result

Theresultsofpartaandpartbare.ln(y)=a+bln(z)=a+bSo,lnz=lnyy=zTherefore,ea+b=eaeb

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