Greenwood press

LOGARITHMS
55

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tudes, with stars ranked “1” as the brightest. Astronomers using powerful tele-
scopes have increased this star-magnitude scale to 29. Analysis of the quantity of
light that reaches the viewer indicates that the star-magnitude scale is logarith-
mic. In the nineteenth century, the scale was standardized so that a difference of
5 magnitudes corresponds to 100 times greater light intensity.
Acidity or alkalinity of a substance is measured on the logarithmic scale pH =
–log(H
+
), where H
+
is the concentration of hydrogen ions in moles per liter of the
substance. These pH units provide a more compact scale than moles per liter. The
scale ranges from 0 to 14, with 7 representing a neutral substance (water). Higher
pHs indicate alkalinity, and lower indicate acidic substances. Few plants will sur-
vive in soils more acidic than pH = 4 (the acidity of lemon juice) or more alkaline
than pH = 8 (baking soda). Battery acid (pH 1) and lye (pH 13) will burn your
skin. Litmus papers turn different colors depending on the pH of the substance. A
change in color that represents 2 levels of pH will represent a difference of 100
times the concentration of H
+
ions.
The Richter scale is a measure of the strength of earthquakes. An earthquake
with a Richter scale value of 4 feels like vibration from a passing train. A scale
value of 7 indicates an earthquake that produces ground cracks and causes
houses to collapse. Because the scale is logarithmic, the difference in energy
from the earthquake waves is 10
7−4
= 1,000. An earthquake measured as a 7 on
the Richter scale is 1000 times more powerful than an earthquake measured at 4.