Solve for k
k=\frac{2^{n}-1}{1001}
Solve for n
n=\log_{2}\left(1001k+1\right)
k>-\frac{1}{1001}
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1001k=2^{n}-1
Swap sides so that all variable terms are on the left hand side.
\frac{1001k}{1001}=\frac{2^{n}-1}{1001}
Divide both sides by 1001.
k=\frac{2^{n}-1}{1001}
Dividing by 1001 undoes the multiplication by 1001.
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