converting the sum of numbers to logarithms If I have three number, $[0.2, 0.3, 0.4]$ then I can take the sum simply by adding the term: $0.2+0.3+0.4=0.9$. The proportion of the first element is then $0.2/0.9 = 2/9$.

Now I don't know what the three numbers are but I do know the logarithms (which are so small I cannot take the exponentiation of it). How can I get the proportion of the elements?

So given: $[-1.6094,   -1.2040,   -0.9163]$, how do I find out that the first component has a proportion of $2/9$?
If this is a practical problem then note you can use an arbitrary precision floating point library ( like MFPR , which is free ) to write a short application to do the exponentiation and addition and division to any precision you care to.
If this is a practical problem then note you can use an arbitrary precision floating point library ( like MFPR , which is free ) to write a short application to do the exponentiation and addition and division to any precision you care to.