- #1

Krushnaraj Pandya

Gold Member

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## Homework Statement

## \lim x-a \frac {{a^x-{x^a}}}{{x^x}-{a^a}} = -1## then a is?

## Homework Equations

L'Hospital rule

## The Attempt at a Solution

Using LHR we can write numerator as ##\frac{a^x ln{a}-ax^{a-1}}{x^xln(x+1)}##

plugging x=a and equating to -1 gives 1-ln(a)=ln(a+1); so 1=ln(a(a+1)) but this gives an incorrect answer. Where am I going wrong?