More Powers Above

Calculus Level 5

For positive integers \(A,B,C,D\) , we have

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

equals to

\[ \frac {2^A}{1 + B ( \ln 2)^2 + C \cdot ( \ln 2) } + 2^D \cdot \ln 2 \]

What is the value of \(A + B + C - D \)?

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