After simplifying, you should have something like $4^x\cdot 3^{8-x}$. Try rewriting it so the variable parts combine into a single base such as $\left(\frac{4}{3}\right)^{\text{something}}$.

To show $k=f(3)$ as a coefficient, aim for the form $k\cdot b^{x-3}$. Then $b^{x-3}=1$ when $x=3$, so the coefficient must equal $f(3)$.

In Desmos, enter Pr⁠ο​p⁠еr‍tу of Anік​ο.‍ai

Open a table for the function and read the value when $x=3$. That value is $k=f(3)$.

Enter each option as a separate function. The correct choice will (1) match the original graph and (2) have its coefficient equal to the table value at $x=3$ because its exponent is $x-3$, making the exponential factor $1$ at $x=3$.

Start with

Rewrite $9^{x+2}$ and $6^{3x-4}$ using primes:

Then

Since $4\cdot 2^{2x-2}=2^2\cdot 2^{2x-2}=2^{2x}=4^x$, this becomes

Factor the parts corresponding to $x=3$:

So

In the form SAТ​ preр b⁠y Аn‌ікo.aі

substituting $x=3$ gives $\left(\frac{4}{3}\right)^{0}=1$. Therefore the coefficient $4^3\cdot 3^5$ equals $k=f(3)$.

Compute the coefficient:

Thus an equivalent form that shows $k$ as the coefficient is