High-Precision Logarithm

Find the Napierian logarithm of $\frac{1001}{999}$ correct to sixteen places of decimals.

~10 minAnswer checked instantlylogarithmic seriesnumerical approximation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 6

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).