Calculating Minimum Average Cost

Question

The question asks,

The cost of producing x units of a product is given by

$C(x)=800+80x−80ln(x)$, $x≥1$.

Find the minimum average cost.

I keep getting $\$880$ as the minimum average cost but it isn't the right answer. Can anyone explain why?

Answer 1

$$C(x)=800+80x−80ln(x)$$

$$ \bar C =C(x)/x=800/x+80−80ln(x)/x$$

$$ \bar C' =-800/(x^2)−80(1-ln(x))/(x^2)$$

$$ \bar C' = 0 \implies -800−80(1-ln(x))=0$$

Solve for $x$ and evaluate your average cost at $x$