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lim x--> 2+ (5(x-2))^(x-2)

so what i did i let y= that limit

Then i took the natural log:

lim x --> 2+ (x-2) ln| (5(x-2))

then i put it in the form of L'hopitals rule:

lim x--> 2+ (ln |(5(x-2))) / 1/(x-2) ...when i plug in 2 for x, both equations DNE so it fits the rule

So i get the function [5(5x-10)^-1] / [ -(x-2)^-2]

I just find that by looking at what the equation is, every time i apply l'hopitals rule, it will just keep growing within the negative powers.. I am not sure what to do, if i did something wrong, or what i should try?