Logarithm problem


A table of the function y = log x contains entries for x = 1 to x = 10 at intervals of 0.001.
Values intermediate to each pair of consecutive entries are to be computed by linear interpolation.
Assume the entries in the table are exact.
a. Show that the error in linear interpolation will not exceed & in the sixth decimal place.
b. For what values of x will linear interpolation be satisfactory for a seven-place table?

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