Prime equals triple prime?

Calculus Level 3

f(x)=f(x) f'(x) = f'''(x)

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

f(1)=6,f(1)=5,f(1)=3 f(1) = 6, f'(1) = 5, f''(1) = -3

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

Details and Assumptions

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

Image Credit: Wikimedia Taylor Series
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