How to interpret "LDA effect size"

What is exactly is meant by LDA effect size? Is it like a ratio of LDA scores for a taxon in relation to 2 different classes?

For example, what is meant by a LDA(log10) score of 2? Does this imply a 100x effect?

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The LDA effect size can generally be thought of as an order of magnitude difference in abundance. (See how it is interpreted in the original paper:
To get more specific about what is being done, the same paper offers the following:
“An LDA model is finally built with the class as dependent variable and the remaining feature values, subclass, and subject values as independent variables. This model is used to estimate their effect sizes, which are obtained by averaging the differences between class means (using unmodified feature values) with the differences between class means along the first linear discriminant axis, which equally weights features’ variability and discriminatory power. The LDA score for each biomarker is obtained computing the logarithm (base 10) of this value after being scaled in the [1,106] interval and, regardless of the absolute values of the LDA score, it induces the ranking of biomarker relevance. For robustness, LDA is additionally supported by bootstrapping (default 30-fold) and subsequent averaging.”

I hope that helps!