Difference between revisions of "-log(1-x) less than x/(1-x)"
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(Created page with "==Theorem== The following formula holds for $x<1$ and $x\neq 0$: $$-\log(1-x) < \dfrac{x}{1-x},$$ where $\log$ denotes the logarithm. ==Proof== ==References== * {{BookRe...") |
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=X less than -log(1-x)|next= | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=X less than -log(1-x)|next=abs(log(1-x)) less than 3x/2}}: $4.1.34$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 19:53, 25 June 2017
Theorem
The following formula holds for $x<1$ and $x\neq 0$: $$-\log(1-x) < \dfrac{x}{1-x},$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.34$
