Consider equations xlogy⁡x=2 and ylogx⁡y=16The value of x isThe value of y is

let  logy⁡x=tthen x=yt---1now ,xlogy⁡x=2 becomesxt=2x=21/t-----2and ylogx⁡y=16 becomesy1/t=24y=24t------3Putting the values of x and y in (1), we get     21/t=24t2⇒     4t3=1∴ t=141/3----4Using (4) and (2), we get  x=(2)(4)1/3=243Using (4) and (3), we get y=(2)(4)2/3=2163let  logy⁡x=tthen x=yt---1now ,xlogy⁡x=2 becomesxt=2x=21/t-----2and ylogx⁡y=16 becomesy1/t=24y=24t------3Putting the values of x and y in (1), we get     21/t=24t2⇒     4t3=1∴ t=141/3----4Using (4) and (2), we get  x=(2)(4)1/3=243Using (4) and (3), we get y=(2)(4)2/3=2163