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If x had dimensions of metres, say, then you can't have x=2m or whatever because dimensions can't be put into the equation to give log(2m).

What about if you have x1=4m and x2=2m and put

log(4m)-log(2m)

Each term doesn't exist by itself, but using log laws, this would be log(4m/2m)=log(2).

So how can they exist together but not by themself?