What is the exact value of the exponential equation

4 (10)^(5x) = 200       divide both sides by 4

(10)^(5x) = 50          take the log of both sides

log 10^(5x) = log 50       and by a log property, we can write

(5x) log 10  =  log 50        log 10  = 1  ....so we can ignore this.....and we have

5x  =  log 50             divide both sides by 5

x =  [ log 50 ] / 5