Answer:
ln(y) = 0.264x -2.748
Explanation:
You want a logarithmic equation that relates the given table of diameters (y) to the length in inches (x) of common nails.
Regression
A graphing calculator can find "best fit" values for an equation you might choose for the representation. A linear approximation to ln(y) is shown in the attachment.
ln(y) = 0.264x -2.748
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Additional comment
The best approximation of a relation between x and y that we have found is a linear approximation y = ax+b. (R²=0.9958) A quadratic approximation to ln(y) is almost as good. (R²=0.9918) The linear approximation of ln(y) shown above is not a particularly good one.
In short, the relation between length and diameter does not seem to be logarithmic.