\(\displaystyle{\ln{{r}}}+{\ln{{q}}}={k}{r}\) Isolating \(\displaystyle{r}\)

monkeyman130yb

monkeyman130yb

Answered question

2022-03-28

lnr+lnq=kr Isolating r

Answer & Explanation

shvatismop1rj

shvatismop1rj

Beginner2022-03-29Added 10 answers

Recall that
logz=W(z)+logW(z) (1)
where W is Lambert's "W" function.
Here, we have
logr+logq=krlogq=kr+logr (2)
So, let's add log(k) to both sides of (1) to obtain
log(kq)=(kr)+log(kr) (3)
Comparing (3) with (1) reveals that
r=1kW(kq)
NOTE:
If we are restricting k,r, and q to be real-valued, then we must have
kqe1.

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