Subtracting powers with variable in exponent I am having some troubles with a question that subtracts powers.

Solve for unknown:
$$3^{x+4} - 5(3^x) = 684$$

I have a hunch that I should apply factorization somehow. Do I multiply 5 and 3 to begin or should I change to logarithm form and have the 5 act as an exponent on $3^x$, and then factorize? 

Any recommendations are appreciated!
I'm not sure if you mean $3^{x+4}-5(3^x)=684$ or $3^x+4-5(3^x)=684$.  If you mean the first, then rewrite $3^{x+4}$ as $3^x\cdot3^4$ and then factor $3^x$ out.  If you mean the second way, subtract $4$ from each side and then factor out $3^x$.  Hope this helps.
You factor out the $3^x:$
$(3^4-5)(3^x)=680$
$\longrightarrow$
$76(3^x)=680$
Now, you can solve this equation with calculator.