$f(x) = ab^x$ where $a$ and $b$ are positive constants. $f(5) = 96, f(7) = 384$. What is the value of $a$? What I've figured out so far:
$$
\begin{align}
ab^5 &= 96\\
ab^7 &= 384\\
\frac{384}{96} &= 4\\
4(ab^5) &= ab^7\\
4a\cdot 4b^5 &= ab^7\\
3a\cdot 4b^5 &= b^7\\
3a\cdot 4 &= b^2\\
12a &= b^2
\end{align}
$$
?????

If you plug in $f(5)=96$, you will get $$96=ab^5 \tag{A}$$
If you plug in $f(7)=384$, you will get $$384=ab^7 \tag{B}$$
Now, $(\text{B})$ divided by $(\text{A})$ yields $$\frac{386}{84}=\frac{ab^7}{ab^5}$$
and simplifying the above equation gives $$4=b^2$$ Thus $\boxed{b=\pm2}$. 
Plug in $b=\pm2$ into either $(\text{A})$ or $(\text{B})$ (I choose $(\text{A})$ below):
$$96=a(\pm2)^5$$ and you will get $\boxed{a=\pm3}$.
