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Correlation on log-log? -or- Easy way of removing 0's?

I have been creating scatter plots on a log-log graph, and they look
pretty good.

However, I'd like some more accuracy than saying "pretty good". I tried
to use CORRELATE, and got some fairly reasonable values. However, since
CORRELATE is working with the pure data, scatters that look good on the
log-log plot can give some pretty horrendous correlation coefficients.

Therefore, I thought I'd try doing a correlation of the log the data, to
get a better impression of what I'm seeing. Of the five data sets, 2
gave better correlations, one got worse, and 2 gave me NaN's.

I think that this may be because some of the values are 0, and this
makes my computer explode (metaphorically speaking, of course). Is there
an easy way of fixing this problem without loops? Could there be another
cause of my problem?