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Mathematics and Log Functions

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To illustrate:

b^xT - b^xA [approximately equal to] (log b)b^xT (x_T - x_A)
Rel(b^xA) [approximately equal to] (log b)x_T Rel(x_A)(*)
k = (log b)x_T (**)

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Compare pi^100 to pi^100.1. Calculate these directly as accurately as you can. Then calculate Rel(pi^100.1) directly using (*). Also give the condition number k of (**).

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Solution Preview

Please see the attachment.

Using Mathematica, we find pi^100 is approximately 5.18785 x 10^49 and pi^100.1 ...

Solution Summary

We use Mathematica to compute pi^100 and pi^100.1 to six significant figures and compute the relative error of pi^100.1 with respect to pi^100.