(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

L'Hospital rule

3. 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?

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# Limit problem

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