Abs(log(1+z)) less than or equal to -log(1-abs(z))

Theorem

The following formula holds for $|z|<1$: $$\left| \log(1+z) \right| \leq - \log(1-|z|),$$ where $\log$ denotes the logarithm.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.38$