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Evaluate: lim(x->2)(x-2)/((log)a(x-1))...

Evaluate: `lim_(x->2)(x-2)/((log)_a(x-1))`

Text Solution

Verified by Experts

`underset(xto2)lim(x-2)/(log_(a)(x-1))" "`(0/0 from)
`=underset(xto2)lim(x-2)/(log_(a){1+(x-2)}}`
`=underset(hto0)lim(x-2)/(log_(e)(1+h))log_(e)a" "`(Substituting x-2=h)
`log_(e)a`
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