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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](https://tex.z-dn.net/?f=%5Csqrt%7B%5Clog_%7B2%7D%7Bx%5E%7B4%7D%7D%7D%2B4%5Clog_%7B2%7D%7B%5Cleft%28%5Csqrt%5B4%5D%7B%5Cdfrac%7B2%7D%7Bx%7D%7D%5Cright%29%7D%3D2%5C%5C%5Csqrt%7B4%5Clog_%7B2%7Dx%7D%2B4%5Clog_%7B2%7D%5Cleft%28%5Cdfrac%7B2%7D%7Bx%7D%5Cright%29%5E%7B1%2F4%7D%3D2%5C%5C2%5Csqrt%7B%5Clog_%7B2%7D%7Bx%7D%7D%2B%5Cdfrac%7B4%7D%7B4%7D%5Clog_%7B2%7D%7B%5Cdfrac%7B2%7D%7Bx%7D%7D%3D2%5C%5C2%5Csqrt%7B%5Clog_%7B2%7D%7Bx%7D%7D%2B%5Clog_%7B2%7D%7B2%7D-%5Clog_%7B2%7D%7Bx%7D%3D2%5C%5C2%5Csqrt%7B%5Clog_%7B2%7D%7Bx%7D%7D%2B1-%5Clog_%7B2%7D%7Bx%7D%3D2%5C%5C2%5Csqrt%7B%5Clog_%7B2%7D%7Bx%7D%7D-%5Clog_%7B2%7D%7Bx%7D%3D1%5C%5C%5Clog_%7B2%7D%7Bx%7D%3Da%2C%5C%5C%5C%5C2%5Csqrt%7Ba%7D-a%3D1%5C%5C2%5Csqrt%7Ba%7D%3D1%2Ba%5C%5C4a%3D%281%2Ba%29%5E2%5C%5C4a%3D1%2B2a%2Ba%5E%7B2%7D%5C%5Ca%5E%7B2%7D-2a%2B1%3D0%5C%5C%28a-1%29%28a-1%29%3D0%5C%5Ca%3D1%5C%5C%5Clog_%7B2%7D%7Bx%7D%3D1%5Cequiv2%5E%7B1%7D%3Dx%5Crightarrow+x%3D2 "\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](https://tex.z-dn.net/?f=%5Clog%7Bx%5E%7B2%7D%7D%3D%5B%5Clog%28x%29%5D%5E%7B2%7D%5C%5C2%5Clog%7Bx%7D-%5B%5Clog%7Bx%7D%5D%5E%7B2%7D%3D0%5C%5C%5Clog%7Bx%7D%3Da%2C%5C%5C2a-a%5E%7B2%7D%3D0%5C%5Ca%282-a%29%3D0%5C%5Ca%3D0%5Chspace%7B5mm%7Da%3D2%5C%5C%5Clog%7Bx%7D%3D0%5Chspace%7B5mm%7D%5Clog%7Bx%7D%3D2%5C%5Cx%3D1%5Chspace%7B5mm%7Dx%3D100 "\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")
para el siguiente,
kellijaeli11:
gracias amigoo :)
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