logs

No way to get the bases equal...so  take the log of both sides and  by a log property we  can write

(x + 3) log 4   = x log 7

x log 4  +  3 log 4 =  x log 7

x ( log 4 - log7)   =  - 3 log 4

x = ( -3 log 4)  /(log 4 - log 7)  ≈  7.43