[tex]\log _2\left(x\right)+\log _x\left(2\right)=2 \\ \log _2\left(x\right)+\frac{\log _2\left(2\right)}{\log _2\left(x\right)}=2 \\ \log _2\left(x\right)+\frac{1}{\log _2\left(x\right)}=2 \\ \log _2\left(x\right)=u \\ u+\frac{1}{u}=2 \\ u=1\log _2\left(x\right)=1 \\ \log _2\left(x\right)=\log _2\left(2\right) \\ x=2[/tex]
