Prove that for sufficiently large $x$, $(\log x)^p<x$ where $p$ is a positive integer.
1840
How can I prove that $\log^k(n) = O(n^\epsilon)$?
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
117262
Proving a logarithm inequality
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
51671
lower bounding logarithm of sums
149889
Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$
148376
Proving that a Binary Tree of $n$ nodes has a height of at least $\log(n)$.
16660
Prove that any positive number has an $n$th root
26962
Proving an inequality involving the logarithm function: $\frac{1}{n+1} \leq \ln \left(1+\frac 1n\right) \leq \frac 1n$
110146
I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
129584
How prove $E|X|^p<\infty$ and $E|Y|^p<\infty$, if $E|X+Y|^p<\infty$
78356
How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$
67851
Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
139383
Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.