Ответы на вопрос:
1)
решаем методом рационализации
ответ : х=1
2)
ответ : х= 5
3)
0\\\\(log_24+log_2x)^2+(log_22+log_2x)^2=1\\\\(2+log_2x)^2+(1+log_2x)^2=1\\\\4+4log_2x+log_2^2x+1+2log_2x+log_2^2x=1\\\\2log_2^2+6log_2x+4=0\\\\log_2x=-1; log_2x=-2\\\\x=1/2; x=1/4" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20log_2%5E2%284x%29%2Blog_2%5E2%282x%29%3D1%5C%5C%5C%5CODZ%3A%20x%3E0%5C%5C%5C%5C%28log_24%2Blog_2x%29%5E2%2B%28log_22%2Blog_2x%29%5E2%3D1%5C%5C%5C%5C%282%2Blog_2x%29%5E2%2B%281%2Blog_2x%29%5E2%3D1%5C%5C%5C%5C4%2B4log_2x%2Blog_2%5E2x%2B1%2B2log_2x%2Blog_2%5E2x%3D1%5C%5C%5C%5C2log_2%5E2%2B6log_2x%2B4%3D0%5C%5C%5C%5Clog_2x%3D-1%3B%20log_2x%3D-2%5C%5C%5C%5Cx%3D1%2F2%3B%20x%3D1%2F4" title="\displaystyle log_2^2(4x)+log_2^2(2x)=1\\\\ODZ: x>0\\\\(log_24+log_2x)^2+(log_22+log_2x)^2=1\\\\(2+log_2x)^2+(1+log_2x)^2=1\\\\4+4log_2x+log_2^2x+1+2log_2x+log_2^2x=1\\\\2log_2^2+6log_2x+4=0\\\\log_2x=-1; log_2x=-2\\\\x=1/2; x=1/4">
4)
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