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Question #44f58

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Jan 7, 2017

#log(7/5)#

Explanation:

#x^7-1=(x-1)(1+x+x^2+cdots+x^6)#
#x^5-1=(x-1)(1+x+x^2+cdots+x^4)#

so

#(x^7-1)/(x^5-1)=(1+x+x^2+cdots+x^6)/(1+x+x^2+cdots+x^4)#

then

#lim_(x->1)log((x^7-1)/(x^5-1))=log(lim_(x->1)(1+x+x^2+cdots+x^6)/(1+x+x^2+cdots+x^4))=log(7/5)#

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