Question Number 208097 by efronzo1 last updated on 05/Jun/24
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Answered by MM42 last updated on 05/Jun/24
$$\mathrm{2}^{{x}−{m}+\mathrm{1}} −\mathrm{2}^{{x}−{m}} \:=\mathrm{8} \\ $$$$\Rightarrow\mathrm{2}^{{x}−{m}} =\mathrm{8}\Rightarrow{x}−{m}=\mathrm{3}\Rightarrow{x}={m}+\mathrm{3} \\ $$$$\Rightarrow\left(\mathrm{2}{m}+\mathrm{3}\right)^{\left(\mathrm{2}{m}+\mathrm{3}\right)^{\mathrm{2}} } =\mathrm{2} \\ $$$$\Rightarrow\mathrm{2}{m}+\mathrm{3}=\sqrt{\mathrm{2}} \\ $$$$\Rightarrow{m}=\frac{\sqrt{\mathrm{2}}−\mathrm{3}}{\mathrm{2}}\:\:\&\:\:{x}=\frac{\sqrt{\mathrm{2}}+\mathrm{3}}{\mathrm{2}}\:\: \\ $$$$ \\ $$