Question Number 145108 by imjagoll last updated on 02/Jul/21
Answered by liberty last updated on 02/Jul/21
$$\:\sqrt[{\mathrm{1}/\mathrm{4}}]{\:\sqrt[{\mathrm{1}/\mathrm{5}}]{\frac{\mathrm{2}^{{x}+\mathrm{1}} }{\mathrm{32}^{\mathrm{2}{x}−\mathrm{2}} }}}=\:\mathrm{64} \\ $$$$\Rightarrow\:\sqrt[{\mathrm{1}/\mathrm{4}}]{\:\left(\frac{\mathrm{2}^{{x}+\mathrm{1}} }{\mathrm{2}^{\mathrm{10}{x}−\mathrm{10}} }\right)^{\mathrm{5}} }=\:\mathrm{2}^{\mathrm{6}} \\ $$$$\Rightarrow\left(\mathrm{2}^{−\mathrm{9}{x}+\mathrm{11}} \right)^{\mathrm{20}} \:=\:\mathrm{2}^{\mathrm{6}} \\ $$$$\Rightarrow\left(\mathrm{11}−\mathrm{9}{x}\right)=\frac{\mathrm{10}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{9}{x}\:=\:\frac{\mathrm{23}}{\mathrm{3}}\:;\:{x}=\frac{\mathrm{23}}{\mathrm{27}}.\: \\ $$