3^n=513

3^n = 513 ....    let's just take the log of both sides....so we have

log 3^n  = log 513    and by a log property we can write

n * log 3   =  log 513           divide both sides by log 3

n = log 513  / log 3      

And you can evaluate the right side for yourself with a calculator....

{Hint......the answer should be between 5 and 6 }