Question

\((\log_{2} (4x))^2-\log_{\sqrt{}2} (2x)=5\)

Answer 1

\(\left[log_24x\right]^2-log_{\sqrt{2}}2x=5\)

=>\(\left[log_2\left(2\cdot2x\right)\right]^2-log_{2^{\dfrac{1}{2}}}2x=5\)

=>\(\left[1+log_22x\right]^2-1:\dfrac{1}{2}\cdot log_22x=5\)

=>\(\left(log_22x\right)^2+2\cdot log_22x+1-2\cdot log_22x=5\)

=>\(\left(log_22x\right)^2=4\)

=>\(\left[{}\begin{matrix}log_22x=2\\log_22x=-2\left(loại\right)\end{matrix}\right.\Leftrightarrow log_22x=2\)

=>\(2x=2^2=4\)

=>x=2