Having trouble with a log question, help would be appreciated

(Log(x^2)+Log(x^4))/Log(50x)=3   multiply both sides by log(50x)....simplify the right side

log(x^2 * x^4)   = 3 log(50x)      and by  log properties, we can write

log(x^6)  = log (50x)^3     and we can solve this

x^6  = (50x)^3

x^6  = (50)^3  * x^3    divide both sides by x^3

x^3  = (50)^3     and it's obvious that x = 50