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Can someone explain why the TI-82 cannot correctly evaluate the expression

6.595744681^(1/log 6.595744681)

(that is log base 10)
The correct answer is 10, but the TI-82 gives 3E-15.

A colleague of mine stumbled across this while graphing the function

y1=x^(1/log x)

in the window [0,10]x[0,10]. y1 is just the constant function y=10 for x>0,
in disguised form. However the graph juts down to the value 3E-15 at

x=6.595744681
To see this, trace to the anomolous point, then quit the graphing window,
enter the expression

X

and then check the calculation

X^(1/log X)

(Note: if you just use the approximation for  X given in the viewing window,
i.e. X = 6.5957447, then x^(1/log x) gives the correct value 10).

This phenomenon can also be found at some other values of x. For example,
graph y1 in the windows [0,100]x[0,10] or (even more startling)
[0,101]x[0,10]. Other examples can be found by zooming in using zbox around
the anomaly.


Russell Blyth
Saint Louis University
blythrd@sluvca.slu.edu