Here is a good read on how fold-changes are calculated: http://www.nature.com/ng/journal/v32/n4s/pdf/ng1032.pdf

In your case, if a 1.5 fold change is the threshold, then up regulated genes have a ratio of 0.58, and down regulated genes have a ratio of -0.58.

log2FC = log2(B) - log2(A)
FC = 2 ^ log2FC

As it says in the linked article, log transformed fold changes are nicer to work with because the transform is symmetric for reciprocals. That means, log2(X) = -1 * log2(1/x), so it is much easier to understand. Either way is equivalent, but the log transform makes it more clear.

I really like the explanation on Wikipedia page:

In the field of genomics (and more generally in bioinformatics), fold changes are defined directly in terms of ratios. If the initial value is A and the final value B, the fold change is defined as B/A. Note that this is different to the definition described above.In other words, a change from 30 to 60 is defined as a fold-change of 2. This is also referred to as a "2-fold increase". Similarly, a change from 30 to 15 is referred to as a "2-fold decrease".In genomics, log ratios are often used for analysis and visualization of fold changes. The log2 (log with base 2) is most commonly used. For example, on a plot axis showing log2-fold-changes, an 8-fold increase will be displayed at an axis value of 3 (since 2^3 = 8).

And this paper: Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2