X/(1+x) less than log(1+x)

Theorem

The following formula holds for $x>-1$: $$\dfrac{x}{1+x} < \log(1+x),$$ where $\log$ denotes the logarithm.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.33$