I don't understand the formula for the Zech logarithm. How do you compute it by hand?

On Wikipedia: theZech logarithmof an integernmay be defined such that

α^[Z(n)] = 1 + α^n

Given q=2^3and an irreducible polynomial α^3+ α + 1, how do you find the Zech log vector {-infinity,0,3,6,1,5,4,2} ?

Thanks for any kind of help provided.