New posts in Exponential Function

How do I show $(e^{x^2}-1)(e^{y^2}-1) \geq (e^{xy}-1)^2$ for all $x,y> 0$?

A tricky inequality: $n(n+1)^{\frac{1}{n}}+(n-2)n^{\frac{1}{n-2}}>2n,\ n\geq3.$

Integral $\int_0^y \exp\left( \alpha x + \frac{1}{1-\beta e^{\gamma x}}-\frac{1/\beta }{ 1-\beta e^{-\gamma x}}\right)dx$

Find all $x\in\mathbb{R}$ such that $\left( \sqrt{2-\sqrt{2} }\right)^x+\left( \sqrt{2+\sqrt{2} }\right)^x=2^x$.

How can we prove that there is a number $a$ such that $\lim_{h\to 0}\frac{a^{h} -1}{h}=1$?

Why is $f(t) = e^{ta}$ differentiable in a unital Banach algebra?

A very interesting question: intersection point of $x^y=y^x$

how would you prove that polynomial functions are not exponential?

Find the value of $a$ where $a^x = \frac{\log(x)}{\log(a)}$ has only one solution

What is it called when $x$ grows at a rate of $x^2$?