Your algebra looks good, my calculator gives
Solve for :
So if I transform this into log form
I should have Log(4^4x-8)=log(3^7x-2)
(4x-8)log(4)=(7x-2)log(3)
4log(4)x-8log(4)=7log(3)x-2log(3)
4log(4)x-7log(3)x=8log(4)-2log(3)
then solve for x= 8log(4)-2log(3) /4log(4)-7log(3) = -4.16?