0;\\
6\cdot6^x-6^2x>0;\\
6^x=k(k\geq0)==>6k-k^2>0;\\
k(6-k)>0==>6^x=k\ \in(0;6)\\
D(f):\ x\in(1;+\infty);\\
0<\frac1{\sqrt{5}}<1==>\\
==>\left(\frac1{\sqrt5}\right)^{\log_{\frac{1}{\sqrt{5}}}\left(6^{x+1}-36^x\right)}\leq\left(\frac1{\sqrt5}\right)^{-2};\\
6^{x+1}-36^x\leq\left(5^{-\frac12}\right)^{-2};\\
6^{x+1}-36^x\leq5^{(-\frac12)\cdot(-2)};\\
6^{x+1}-36^x\leq5;\\
6^x=t:\ t\geq0;\\" alt="\log_{\frac{1}{\sqrt{5}}}\left(6^{x+1}-36^x\right)\geq-2;\\
D(f):6^{x+1}-36^x>0;\\
6\cdot6^x-6^2x>0;\\
6^x=k(k\geq0)==>6k-k^2>0;\\
k(6-k)>0==>6^x=k\ \in(0;6)\\
D(f):\ x\in(1;+\infty);\\
0<\frac1{\sqrt{5}}<1==>\\
==>\left(\frac1{\sqrt5}\right)^{\log_{\frac{1}{\sqrt{5}}}\left(6^{x+1}-36^x\right)}\leq\left(\frac1{\sqrt5}\right)^{-2};\\
6^{x+1}-36^x\leq\left(5^{-\frac12}\right)^{-2};\\
6^{x+1}-36^x\leq5^{(-\frac12)\cdot(-2)};\\
6^{x+1}-36^x\leq5;\\
6^x=t:\ t\geq0;\\" align="absmiddle" class="latex-formula">
t\in(-\infty;1]\cup[5;+\infty)\cap(0;6)==>\\
==>t\in(0;1]\cup[5;6);\\
x\in(-\infty;0]\cup[\log_65;1)" alt="6t-t^2\leq5;\\
t^2-6t+5\geq0;\\
D=(-6)^2-4\cdot1\cdot5=36-20=16=(\pm4);\\
t_1=\frac{6-4}{2}=1\in(0;6);\\
t_2=\frac{6+4}{2}=5\in(0;6);\\
6^{x_1}=1;\\
x_1=0;\\
6^{x_2}=5;\\
x_2=\log_65;\\
t^2-6t+5\geq0==>t\in(-\infty;1]\cup[5;+\infty)\cap(0;6)==>\\
==>t\in(0;1]\cup[5;6);\\
x\in(-\infty;0]\cup[\log_65;1)" align="absmiddle" class="latex-formula">