3 la puterea 37 minus 27 la puterea 12 egal cu 2 ori 81 la puterea 10 împărțit la x la puterea a doua
____________________
3^37 - 27^12 = 2 · 81^10 : x^2
_____________________
[tex]\it 3^{37}-27^{12}=2\cdot81^{10}:x^2 \Rightarrow 3^{37}-(3^3)^{12}=2\cdot(3^4)^{10}:x^2 \Rightarrow\\\\\Rightarrow 3\cdot3^{36}-3^{36} =2\cdot3^{40}:x^2 \Rightarrow 3^{36}(3-1)=2\cdot3^{40}:x^2\Rightarrow \\ \\\Rightarrow 2\cdot3^{36}=2\cdot3^{40}:x^2|_{:(2\cdot3^{36})} \Rightarrow 1 = 3^4:x^2 \Rightarrow1=81:x^2 \Rightarrow \\ \\ \Rightarrow x^2=81 \Rightarrow \sqrt{x^2}=\sqrt{81} \Rightarrow |x| =9 \Rightarrow x = \pm9[/tex]
