[tex]\it log_2x+log_4x+log_8x=\dfrac{11}{6} \Leftrightarrow log_2x+\dfrac{log_2x}{log_24}+\dfrac{log_2x}{log_28}=\dfrac{11}{6} \Leftrightarrow \\ \\ \\ \Leftrightarrow log_2x\cdot(1+\dfrac{1}{2}+\dfrac{1}{3})=\dfrac{11}{6} \Leftrightarrow log_2x\cdot\dfrac{11}{6}=\dfrac{11}{6}\Big|_{:\dfrac{11}{6}} \Leftrightarrow log_2x=1 \Leftrightarrow x=2[/tex]
