Prime equals triple prime?

Calculus Level 3

\[ f'(x) = f'''(x) \]

For some infinitely differentiable function \(f(x) \), it satisfies the above equation. Given the initial conditions

\[ f(1) = 6, f'(1) = 5, f''(1) = -3 \]

What is the value of \( f( \ln(42) ) \)?

Details and Assumptions

\( f'(k), f''(k), f'''(k) \) denote the first, second, and third derivative of \(f(x) \) at \(x=k\) respectively.

Image Credit: Wikimedia Taylor Series
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