none of the above (as written)x = 12 (as interpreted)
Step-by-step explanation:
The equation written has two solutions, neither of which is among those listed. There are no algebraic means for solving it, but solutions can be found graphically and by iteration.
 ![\dfrac{320x\left(\dfrac{1}{4}\right)^x}{4}=5\\\\16x\cdot 4^{-x}=1](/tpl/images/0431/3526/5d6f2.png)
With a little more manipulation, this becomes ...
 ![4^{x-2}-x=0](/tpl/images/0431/3526/75b96.png)
It has solutions near x= 0.069 and x = 2.722.
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It looks like you may want your equation to be interpreted to be ...
 ![320\left(\dfrac{1}{4}\right)^{\dfrac{x}{4}}=5\\\\64\left(\dfrac{1}{4}\right)^{\dfrac{x}{4}}=1\\\\\log{(64)}-\dfrac{x}{4}\log{4}=0 \quad\text{take logs}\\\\\left(3-\dfrac{x}{4}\right)\log{4}=0 \quad\text{use $64=4^3$}\\\\12-x=0 \quad\text{multiply by 4, divide by $\log{4}$}](/tpl/images/0431/3526/33017.png)
The exact solution to this interpretation of the problem is x = 12.
![Find the exact solution to the equation.320 x (1/4)^x/4=5 x = 12 x = 13 x = 3 x = 3/4](/tpl/images/0431/3526/0d41e.jpg)