log_{root a}root a{root a[root a( root a (root a ) ) ] }
plsunderstand it no other way to write it

\log_{\sqrt{a}} \sqrt{a \sqrt{a \sqrt{a \sqrt{a \sqrt{a}}}}} = \frac{1}{2} \log_{\sqrt{a}} a \sqrt{a \sqrt{a \sqrt{a \sqrt{a}}}} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{2} \log_{\sqrt{a}} \sqrt{a \sqrt{a \sqrt{a \sqrt{a}}}} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} a \sqrt{a \sqrt{a \sqrt{a}}} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} \sqrt{a \sqrt{a \sqrt{a}}} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} a + \frac{1}{8} \log_{\sqrt{a}} a \sqrt{a \sqrt{a}} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} a + \frac{1}{8} \log_{\sqrt{a}} a + \frac{1}{8} \log_{\sqrt{a}} \sqrt{a \sqrt{a}} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} a + \frac{1}{8} \log_{\sqrt{a}} a + \frac{1}{16} \log_{\sqrt{a}} a \sqrt{a} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} a + \frac{1}{8} \log_{\sqrt{a}} a + \frac{1}{16} \log_{\sqrt{a}} a + \frac{1}{16} \log_{\sqrt{a}} \sqrt{a} = \frac{1}{2} \log_{\sqrt{a}} a + \frac{1}{4} \log_{\sqrt{a}} a + \frac{1}{8} \log_{\sqrt{a}} a + \frac{1}{16} \log_{\sqrt{a}} a + \frac{1}{16} \log_{\sqrt{a}} \sqrt{a} = \frac{1}{2} (2) + \frac{1}{4} (2) + \frac{1}{8} (2) + \frac{1}{16} (2) + \frac{1}{16} (1) = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} = \frac{16 + 8 + 4 + 2 + 1}{16} = \frac{31}{16} ANS . . .

logroot aroot a{root a[root a( root a (root a ) ) ] } plsunderstand it no other way to write it