5) 
0, x \neq 1)\\
2log_x9+2log_9x-5=0\\ \frac{lnx}{ln9} + \frac{ln9}{lnx} - \frac{5}{2} =0\\\\
\frac{2ln^2x+2ln^29-5ln9*lnx}{2ln9*lnx}=0\\(lnx=t)\\
\left \{ {{2t^2-5ln9*t+2ln^29=0} \atop {lnx \neq 0}} \right.
\\(lnx\neq 0<=>x\neq1)\\
t= \frac{5ln9^+_-\sqrt{25ln^29-16ln^29}}{4} =\frac{5ln9^+_-3ln9}{4}\\
t=2ln9=ln81=>x=e^t=e^{ln81}=81\\
t=ln9/2=ln3=>x=e^t=e^{ln3}=3" alt="log_x81+log_9x^2-5=0\\(x>0, x \neq 1)\\
2log_x9+2log_9x-5=0\\ \frac{lnx}{ln9} + \frac{ln9}{lnx} - \frac{5}{2} =0\\\\
\frac{2ln^2x+2ln^29-5ln9*lnx}{2ln9*lnx}=0\\(lnx=t)\\
\left \{ {{2t^2-5ln9*t+2ln^29=0} \atop {lnx \neq 0}} \right.
\\(lnx\neq 0<=>x\neq1)\\
t= \frac{5ln9^+_-\sqrt{25ln^29-16ln^29}}{4} =\frac{5ln9^+_-3ln9}{4}\\
t=2ln9=ln81=>x=e^t=e^{ln81}=81\\
t=ln9/2=ln3=>x=e^t=e^{ln3}=3" align="absmiddle" class="latex-formula">
---
4)I: 
0,x>0)\\
II: \\2log_4x+log_2y=4\\2* \frac{1}{2} log_2x+log_2x=4\\
log_2x+log_2y=log_216\\log_2(xy)=log_216\\xy=16\\
(x^2+y^2)+2*(xy)=32+2*16=64=(x+y)^2\\(x^2+y^2)-2*(xy)=32-2*16=0=(x-y)^2\\
x+y=8 (because x>0, y>0)\\x-y=0=>x=y=4" alt="I: \\log_2(x^2+y^2)=5\\x^2+y^2=2^5=32\\
(y>0,x>0)\\
II: \\2log_4x+log_2y=4\\2* \frac{1}{2} log_2x+log_2x=4\\
log_2x+log_2y=log_216\\log_2(xy)=log_216\\xy=16\\
(x^2+y^2)+2*(xy)=32+2*16=64=(x+y)^2\\(x^2+y^2)-2*(xy)=32-2*16=0=(x-y)^2\\
x+y=8 (because x>0, y>0)\\x-y=0=>x=y=4" align="absmiddle" class="latex-formula">