[tex]\displaystyle log_2x+log_4 \sqrt{x} =5 \\ \\ \frac{log_4x}{log_42} + log_4 \sqrt{x} =5 \\ \\ \frac{log_4x}{log_4 \sqrt{4} } + log_4 \sqrt{x} =5 \\ \\ \frac{log_4x}{ \frac{1}{2}log_44 } + log_4 \sqrt{x} =5 \\ \\ \frac{log_4x}{ \frac{1}{2} } +log_4 \sqrt{x} =5 \\ \\ 2log_4x + \frac{1}{2} log_4x=5 \\ \\ 4log_4x+log_4x=10 \\ \\ 5log_4x=10 \\ \\ log_4x=2\\ \\ log_4x=log_416 \\ \\ x=16[/tex]
