[tex]\displaystyle\bf\\1)\\\\\left(\frac{1}{5}\right)^{2-x}=5\\\\\Big(5^{-1}\Big)^{2-x}=5\\\\5^{-1\cdot(2-x)}=5\\\\5^{x-2}=5^1\\\\x-2=1\\\\x=1+2\\\\\boxed{\bf x=3}\\\\\\2)\\\\2^{3-x}\cdot 8=\frac{1}{2}\\\\2^{3-x}\cdot 2^3=2^{-1}\\\\2^{3-x+3}=2^{-1}\\\\2^{6-x}=2^{-1}\\\\6-x=-1\\\\-x=-1-6~~\Big|\cdot(-1)\\\\ \boxed{\bf x=7}\\\\\\[/tex]
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[tex]\displaystyle\bf\\3)\\\\3^{x+4}=81\\\\3^{x+4}=3^4\\\\x+4=4\\\\x=4-4\\\\\boxed{\bf x=0}[/tex]
