MathBench > Measurement

Logs and pH

And SMALL messy numbers?

Consider an E. coli ... measuring 0.000002 m. It would be easy to say log(0.000001) = −6 ... but E. coli are bigger than that. Not big enough to get to a log E. coliscale number of −5, but about a tenth of the way between − 6 and − 5. If you imagine a number line, you'll see that

a tenth of the way between −6 and −5 = −5.9

number line

So if we do some "unsquishing", we might guess −5.8 or even less. In fact,

log(0.000002) = −5.7 (E. coli)

Likewise, red blood cells have a diameter of 0.000007 m, so they are also between minus 6 and minus 5 on a log scale:

log(0.000007) = −5.2 (red blood cell)

You can tell that E. coli are smaller than red blood cells, because −5.7 is smaller than −5.2.


Now that we know that normal red blood cells are approximately −5.2 on a log scale, we can also guess that a blood cell that is a −4 is going to be very problematic for the poor creature whose capillaries get exploded by it. And a red blood cell that's a −6 will be too tiny to do any good.

RBC and pollen grain

A red blood cell diameter is −5.2 on the log scale, while a typical pollen grain is a −4.5. Which is smaller?

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I think I have the answer: The red blood cell is smaller.