Answer:
- 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.
[tex]\dfrac{320x\left(\dfrac{1}{4}\right)^x}{4}=5\\\\16x\cdot 4^{-x}=1[/tex]
With a little more manipulation, this becomes ...
[tex]4^{x-2}-x=0[/tex]
It has solutions near x= 0.069 and x = 2.722.
____
It looks like you may want your equation to be interpreted to be ...
[tex]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 $\log{4}$}[/tex]
The exact solution to this interpretation of the problem is x = 12.
