x value in the expontential equation 4(10)^5x=200

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

10^(5x)  = 50     take the log of each side

log 10^(5x)  = log50    and we can write

5x log10  = log 50          and log 10   = 1   so we can ignore ths.....and we have...

5x  = log50                  divide both sides by 5

x  = log 50/5 

And you are correct !!!

4*10^(5x)=200

10^(5x)=50

5x=log(50)

x=log(50)/5