# What is a $\log_{10} \%$ transfer?

I have this graph of results comparing the transfer percentages of bacteria to hands with and without gloves. By the looks of things, the higher the bacteria count on the chicken the lower the transfer $\%$. But what's a -ve $\log_{10} \%$ transfer? Is that $(1-10^{-4})100=99.99 \%$? Makes no sense, how could you possibly transfer nearly ALL the (eg $\log 100,000,000 = 8$) bacteria on one surface to your hands? Or am I missing something here?

• as you can see, $\log_{10} \%$ transfer is always less than $2$. a value of $2$ would correspond to $100\%$ transfer. Apr 6, 2013 at 12:55
• in general, the rate is $10^{\log_{10}\% \text{transfer}}\%$, e.g. $10^{-4}\%$ when the exponent is $-4$, and so on Apr 6, 2013 at 13:26
• The vertical scale is the logarithm of the "percent transfer". The horizontal scale is the logarithm of the "CFU on Chicken". Apr 6, 2013 at 13:47

This looks biology. Let's take a look at the horizontal axis. Let the number of CFU on the chicken be $x_{CFU}$. The value on the horizontal axis, moving outwards is on increasing $\log$ of $x_{CFU}$. If $$\log x_{CFU}=7.5$$, then we can see $$x_{CFU} = 10^{7.5}$$. It is an easier way of representing it on a graph.
Similarly, let the percentage transfer be $y_{CFU}$. I'll leave you to do the calculations similar to the above. Let's take this answer one step further with some analysis. If $$\log y_{CFU}=0$$, then $$y_{CFU}=10^0=1\%$$
It seems that for full transfer with bare hands, the number of CFU is around $10^{8.0}$ and $10^{8.5}$. There seems to be an optimum number here.
Also, at the same range on the $x$-axis, wearing gloves reduces the percentage of transfer from above $1\%$ to anywhere between $0.01\%$ and $0.0001\%$. What you can see here is that because those numbers decrease so drastically in orders of $10$, using a logarithmic scale on both axes helps in the readibility of the graph.
• This is a very succinct description, thank you very much. One minor question is regarding the 2log transfer of $10^8$ CFU. That means that 100% is transferred from chicken to hands? Meaning there is no CFU left on the chicken? How is it possible that all the CFU is transferred?