# When to log?

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Hello all,

I have a dataset which I am using to perform some allometric analyses. It's straightforward enough when taking the log10 of single values to plot against each other, but when using the formula for Fulton's condition factor K=(Ms/LT3)*100 where Ms is the somatic body mass and LT is total body length, I am uncertain whether the log transformation should be done on the data being plugged into the formula or on the resulting output from the formula.

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Certainly it is suggested to plot $$y = \log(K)$$ versus $$x = \log( 100M_s/L_T^3) = \log(100M_s) - 3\cdot \log(L_T).$$ The reason being that the latter expression only has linear dependencies, meaning something like $$y = ax+b,$$ as opposed to ratios and exponents that appear in your original. You will obtain a graphical representation which is pleasant to look at, and if you need to do a regreession analysis, these are the points you would want to do it on.

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