Question 2172
Use loga b = 1/logb a,we have
logx 81= 4 converts to
 1/log81 x = 4,
 or log81 x = 1/4,
 Hence, x = (81)^1/4 by definition of logarithm.
 So, x = (81)^1/4 = (3^4)^(1/4) = 3^1 = 3.

  Or use logx 81= log 81/log x = 4, (common logarithm:base 10)
  So,log x = (log 81)/4, 
  x = 10^((log 81)/4) =  10^((log 3^4)/4) = 10^(4(log 3)/4)
    = 10^(log 3) = 3

 Kenny