$ \log_{\sqrt{n}+ \sqrt{n-1}} (\sqrt{n} - \sqrt{n-1}) = $
$ = \log_{\sqrt{n}+ \sqrt{n-1}} (\sqrt{n} - \sqrt{n-1}) + \log_{\sqrt{n}+ \sqrt{n-1}} (\sqrt{n} + \sqrt{n-1}) - \log_{\sqrt{n}+ \sqrt{n-1}} (\sqrt{n} + \sqrt{n-1}) = $
$ = \log_{\sqrt{n}+ \sqrt{n-1}} (\sqrt{n} - \sqrt{n-1}) (\sqrt{n} + \sqrt{n-1}) - \log_{\sqrt{n}+ \sqrt{n-1}} (\sqrt{n} + \sqrt{n-1}) = $
$ = (\log_{\sqrt{n}+ \sqrt{n-1}} (1) ) - 1 = 0 - 1 = -1 $