re-arrange equation L=2^(10(v-1)) v^2

Danika Mckay 2022-10-24 Answered
re-arrange equation L = 2 10 ( v 1 ) v 2
Is it possible to re-arrange this equation to make v the subject?
L = v 2 . 2 10 ( v 1 )
If so, what is the answer?
If it helps (which by excluding zero it should)...
0 < v < 1
I have tried pages of scribbling and got nowhere. In desperation I have tried solving each product separately (easy enough), and then tried to get the right overall result from some combination of L and ( l o g 2 ( L ) + 10 ) / 10 but that hasn't got me anywhere.
I am out of my depth. Please help.
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Answers (1)

latatuy
Answered 2022-10-25 Author has 12 answers
If make v the subject means solve for v, there are solutions in terms of the LambertW function. With Maple I get
v = 1 5 W ( ± 160 ln 2 L ) ln 2
For the ranges 0 < v , L < 1 you have to use the + sign, the will give complex v.
You can also use Wolfram Alpha with the input solve 2 10 ( v 1 ) v 2 = L (they call W the product log function).
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