Consider the vector space P no of polynomials of degree ::5 n. Let/ and g be elements of this space. Prove that the following function satisfies axioms 3 and 4 of the inner product (!, g) = f J(x)g(x)dx (This exercise completes Example 3 of this section, showing that this function is an inner product.)

Math121 Chaapptterr77NNoottess Lesson7.4–PropertiesandApplicationsofLogarithms Thesetipsshouldhelpyougetthroughthishw.J • log (1)=0 x • log (x)=1 • log (a )=rlog (xa x • log (a )=x • a loga(x)=x • log(x)+log(y)=log(xy) • log(x/y)=log(x)–log(y) EXAMPLE1. Usethepropertiesoflogarithmstocondensethefollowing expressionasmuchaspossible,writingtheanswerasasingle termwithacoefficientof1.Allexponentsshouldbepositive. log(y)+log(19) (Usingourtipsatthetopofthepage,we canseethataddingtwologarithmsresu