Problem in Inequality

Question

In a book of " fundamentals of Error-Correcting Codes" by W.Cary Huffman and Vera Pless there is an inequality which used to find Asymptotic Hamming Bound. I need to know how this iniquities hold any help and suggestion will be appreciated Let $ 0<\delta \le 1-q^{-1}$. (a) When $ \delta n >2$ Show that:- $ n \,log_{q}n-\lfloor {\delta n} \rfloor log_{q} \lfloor \delta n \rfloor - (n-\lfloor {\delta n} \rfloor) log_{q} (n-\lfloor \delta n \rfloor)\\ \le - (\delta n -1 ) \times log_{q} (\delta - \frac{1}{n}) + log_{q}n - n(1-\delta) log_{q}(1-\delta) $.