Log(x) less than or equal to n(x^(1/n)-1)
From specialfunctionswiki
Theorem
The following formula holds for $x>0$ and $n>0$: $$\log(x) \leq n \left( x^{\frac{1}{n}} - 1 \right),$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.37$
