- #1
Krushnaraj Pandya
Gold Member
- 697
- 73
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?