# Calculus Proof of inequality: $2015^{2013}<2014^{2014}<2013^{2015}$

I asked this question yesterday and have been working on it. I have to prove that $2015^{2013}<2014^{2014}<2013^{2015}$.

I set $x=2014$, so now I have $$(x+1)^{x-1}<x^x<(x-1)^{x+1}.$$

Since $x^x=\exp(x\log x)$ I have to show that $$(x-1)\log{(x+1)}<x\log x<(x+1)\log{(x-1)}.$$

It's clear to me that $(x-1)< x < (x+1)$, but I don't know how to show that these values are increasing. I've tried taking the derivative values but still not making the connection. What am I missing?