Answer with Explanation:

log 5 512 =log 512/log 5

         =log 2 raised to 9/log (10/2)

         =9 log 2/log 10 - log 2

         =(9 x 0.3010)/1 - 0.3010

         =2.709/0.699 

         =2709/699

         = 3.876