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**lim(x-->inf) of ((x+a)/(x-a))^x = e**

I started this problem and quickly became stuck, the question asks for what value of "a" is the following true:

lim(x-->inf) of ((x+a)/(x-a))^x = e

I took the natural log of both sides to start and got this:

lim(x-->inf) of x*ln((x+a)/(x-a)) = 1

I've tried going on from here but nothing in the end makes sense and i don't know any other way to start the problem; any help is appriciated, thanks.

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