If you meant

2^(x+4) = 4^x

which means 







Since the bases are positive, equal, and not 1,
the exponts are alse equal:





-----------------------------

That's probably what you meant.  But when you don't enclose
the exponent inside of parentheses like this

2^(x+4) = 4^x

then what you wrote

means this:













Then we'd have to use the quadratic formula and 
solve by taking logs and the answer is this complicated
expression:



When typing mathematical expressions and equations, you must
enclose numerators, denominators and exponents in parentheses
except when they contain only one number or only one letter

Edwin