Question

Question #44f58

Answer 1

`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)`