Find the values of \( u \) satistying the equation. \( \log _{4}\left(x^{4}+4\right)=1+\log _{4}\left(x^{2}+4\right) \)

Solve the equation \( \log _{4}\left(x^{4}+4\right)=1+\log _{4}\left(x^{2}+4\right) \). Solve the equation by following steps: - step0: Solve for \(x\): \(\log_{4}{\left(x^{4}+4\right)}=1+\log_{4}{\left(x^{2}+4\right)}\) - step1: Rewrite in terms of common logarithms: \(\log_{4}{\left(x^{4}+4\right)}=\log_{4}{\left(4\left(x^{2}+4\right)\right)}\) - step2: Set the arguments equal: \(x^{4}+4=4\left(x^{2}+4\right)\) - step3: Move the expression to the left side: \(x^{4}+4-4\left(x^{2}+4\right)=0\) - step4: Calculate: \(x^{4}-12-4x^{2}=0\) - step5: Factor the expression: \(\left(x^{2}-6\right)\left(x^{2}+2\right)=0\) - step6: Separate into possible cases: \(\begin{align}&x^{2}-6=0\\&x^{2}+2=0\end{align}\) - step7: Solve the equation: \(\begin{align}&x=\sqrt{6}\\&x=-\sqrt{6}\\&x \notin \mathbb{R}\end{align}\) - step8: Find the union: \(\begin{align}&x=\sqrt{6}\\&x=-\sqrt{6}\end{align}\) - step9: Rewrite: \(x_{1}=-\sqrt{6},x_{2}=\sqrt{6}\) The values of \( x \) that satisfy the equation \( \log _{4}\left(x^{4}+4\right)=1+\log _{4}\left(x^{2}+4\right) \) are \( x=-\sqrt{6} \) and \( x=\sqrt{6} \).