Question

Porfavor me podrian ayudar con esto ejercicios....

Answer 1

tienes,

$\sqrt{\log_{2}{x^{4}}}+4\log_{2}{\left(\sqrt[4]{\dfrac{2}{x}}\right)}=2\\\sqrt{4\log_{2}x}+4\log_{2}\left(\dfrac{2}{x}\right)^{1/4}=2\\2\sqrt{\log_{2}{x}}+\dfrac{4}{4}\log_{2}{\dfrac{2}{x}}=2\\2\sqrt{\log_{2}{x}}+\log_{2}{2}-\log_{2}{x}=2\\2\sqrt{\log_{2}{x}}+1-\log_{2}{x}=2\\2\sqrt{\log_{2}{x}}-\log_{2}{x}=1\\\log_{2}{x}=a,\\\\2\sqrt{a}-a=1\\2\sqrt{a}=1+a\\4a=(1+a)^2\\4a=1+2a+a^{2}\\a^{2}-2a+1=0\\(a-1)(a-1)=0\\a=1\\\log_{2}{x}=1\equiv2^{1}=x\rightarrow x=2$

para el siguiente,

$\log{x^{2}}=[\log(x)]^{2}\\2\log{x}-[\log{x}]^{2}=0\\\log{x}=a,\\2a-a^{2}=0\\a(2-a)=0\\a=0\hspace{5mm}a=2\\\log{x}=0\hspace{5mm}\log{x}=2\\x=1\hspace{5mm}x=100$