More Powers Above

Calculus Level 5

For positive integers A,B,C,DA,B,C,D , we have

limx2xxxx216xxx16 \large \displaystyle \lim_{x \to 2} \frac {x^{x^{x^x}} - 2^{16}}{x^{x^x} - 16}

equals to

2A1+B(ln2)2+C(ln2)+2Dln2 \frac {2^A}{1 + B ( \ln 2)^2 + C \cdot ( \ln 2) } + 2^D \cdot \ln 2

What is the value of A+B+CDA + B + C - D ?

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