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3-x-3-3-x-18-10-x-




Question Number 5522 by Kasih last updated on 17/May/16
3^x +3^(3−x) −18=10  x=?
$$\mathrm{3}^{{x}} +\mathrm{3}^{\mathrm{3}−{x}} −\mathrm{18}=\mathrm{10} \\ $$$${x}=? \\ $$
Answered by Yozzii last updated on 17/May/16
3^x +3^(3−x) −18=10  3^x +((27)/3^x )−28=0  ⇒3^(2x) +27−28(3^x )=0  (3^x )^2 −28(3^x )+27=0  (3^x −1)(3^x −27)=0  ⇒3^x =1,27  ⇒x=0,3.
$$\mathrm{3}^{{x}} +\mathrm{3}^{\mathrm{3}−{x}} −\mathrm{18}=\mathrm{10} \\ $$$$\mathrm{3}^{{x}} +\frac{\mathrm{27}}{\mathrm{3}^{{x}} }−\mathrm{28}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{3}^{\mathrm{2}{x}} +\mathrm{27}−\mathrm{28}\left(\mathrm{3}^{{x}} \right)=\mathrm{0} \\ $$$$\left(\mathrm{3}^{{x}} \right)^{\mathrm{2}} −\mathrm{28}\left(\mathrm{3}^{{x}} \right)+\mathrm{27}=\mathrm{0} \\ $$$$\left(\mathrm{3}^{{x}} −\mathrm{1}\right)\left(\mathrm{3}^{{x}} −\mathrm{27}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{3}^{{x}} =\mathrm{1},\mathrm{27} \\ $$$$\Rightarrow{x}=\mathrm{0},\mathrm{3}. \\ $$$$ \\ $$$$ \\ $$

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