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$f(x)=e^x-x-2=0$ on $[a,b] = [0,3]$

Fixed point iteration $g(x)= \ln(x+2)$ was derived from it with given $x_0=1.5$

how many iterations until $10^{-100}$ accuracy is reached?

I got $(1/2)^{n-1}*|0.247| =< 10^{-100}$

I can't handle this calculation as I get absurd numbers for some reason like 332 on my calculator. What do I do?

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