$f(x) = ab^x$ 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:
$$
\begin{align}
ab^5 &= 96\\
ab^7 &= 384\\
\frac{384}{96} &= 4\\
4(ab^5) &= ab^7\\
4a\cdot 4b^5 &= ab^7\\
3a\cdot 4b^5 &= b^7\\
3a\cdot 4 &= b^2\\
12a &= b^2
\end{align}
$$
?????

Your error is in the line
$$3a \cdot 4b^5 = b^7$$
It appears you've subtracted $a$ from both sides, rather than dividing.

We have
$$\frac{384}{96} = \frac{ab^7}{ab^5} = b^2 \implies b^2 = 4$$
Do you see how to finish from here?
