# Log-log plotting question

I know this is rather simple, but despite my best efforts and quite a bit of searching through google I can't seem to find a satisfactory answer.

An example of what I'm trying to do:

Given a value $N= 6.8\cdot10^{-4}$ and upper and lower errors for that value of $N^{uperr} = 9.1\cdot 10 ^{-4}$ and $N_{lowerr} = 3.9\cdot 10 ^{-4}$

With an equation such as $1.6\cdot 10^{-9}Nx$

How would I go about plotting this point at $x=1$ on a log-log scale, with error-bars given by those I've specified?

Whenever I try to plot this I get error bars which are far too large, since from what I've read online simply adding $N+N^{uperr}$ doesn't work for log-log plots.

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I'll only note that when performing an arbitrary transformation $f(u)$ on an uncertain number of the form $x\pm\epsilon$, the formula you'll need goes like
$f(x\pm\epsilon)=f(x)\pm f^{\prime}(x)\epsilon$