You need to evaluate the limit but first you need to use the logaritmic property to convert the difference of logarithms into the logarithm of quotient:

`lim_(x->1^+) (ln(x^7-1) - ln(x^5-1)) = lim_(x->1^+) ln((x^7-1)/(x^5-1))`

`lim_(x->1^+) ln((x^7-1)/(x^5-1)) = ln lim_(x->1^+)((x^7-1)/(x^5-1)) = ln 0/0`

Since the limit is indetrminate `0/0` , you may use l'Hospital's rule:

`ln lim_(x->1^+)((x^7-1)/(x^5-1)) = ln lim_(x->1^+)(7x^6)/(5x^4) = ln (7/5)`

**Hence, evaluating the limit of the function using l'Hospital's rule yields `lim_(x->1^+) (ln(x^7-1) - ln(x^5-1)) = ln (7/5).` **

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