# How should “7 $\log_{10}$” be interpreted?

A cookery related article I want to refer to mentions a "7 log10 relative reduction of salmonella". A few related sources suggest this evaluates to 10,000,000, although I would have imagined that 107 is the usual way of expressing this.

I initially thought that I should interpret this as log10(7) but that doesn't seem right given that an 85% reduction in salmonella can hardly be considered safe.

If the first interpretation is correct, could someone tell me why it might have been expressed this way, rather than as a power of 10?

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could this perhaps be better asked on Seasoned Advice/Cooking.SE? – Lie Ryan Sep 22 '12 at 13:26

According to this page a 7 log reduction is a reduction in number of microorganisms by 10000000-fold (so $10^7$). It seems like this is something that is often used in food science.

So I guess that the basic idea is that if you draw the relationship between cooking time needed for a certain reduction in organisms and the time, then you get a logarithmic relationship, so maybe that is why they chose to use the log notation to emphasize this fact.

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Notice that:

$$\log_{10} (10,000,000)=7$$

So instead of writing the 1 followed by 7 zeros, that (strange) notation ($7\log_{10}$) might have been used instead. Of course there are other more common notations such as the power and the E.

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