SOlve for 'x' without graphing...5 ^ (3x) = 4 ^ (x+3)

I can use a graphing calculator to deduce that x = 1.2082684. but that isn't "the answer".

3x log 5 = (x+3) log 4
log 5 =(x+3)/3x log 4
log 5/ log 4= (x+3)/ 3x
3x (log 5/log 4)= x+3
3x (log 5/log 4) -x=3
x[(3 log 5/log 4)-1]=3
x=3/[(3 log 5/log 4)-1]