LOGARITHMIC FUNCTIONS are
EVERYWHERE!!
A logarithmic scale uses powers of 10 to compare numbers that vary greatly in size.
For example, they are used to measure the intensity of earthquakes (Richter scale),
measure the alkalinity of a substance (pH scale), and compare sounds (decibel scale).
RICHTER SCALE (Comparing the Intensities of Earthquakes)
The Richter scale uses logarithms to compare the intensity of earthquakes:
True Intensity
101
Richter Scale
Magnitude
log101  1
102
log10 2  2
104
log10 4  4
Example 
An earthquake of magnitude 2 is
actually 10 times more intense than
an earthquake of magnitude 1!!
If the average earthquake measures 4.5 on the Richter scale, determine
how much more intense is an earthquake that measures 8.
 I
M  log  
 Io 
M is the magnitude of the earthquake (Richter number)
I is the intensity of the earthquake being measured
Io is the intensity of the reference earthquake
pH SCALE (Comparing the Alkalinity/Acidity of a Substance)
The pH scale measures the acidity or alkalinity of a substance.
A difference of one pH unit represents a tenfold change in the
concentration of hydrogen ions in a solution (logarithmic scale).
The relationship between pH and hydrogen ion concentration
is given by the formula pH = –log [H+], where H+ is the
concentration of the hydrogen ion in moles per litre.
A pH of 7 indicates a neutral solution.
Any pH under 7 is acidic and any pH over 7 is basic.
Example 
a)
Calculate the pH of a solution with a hydrogen ion concentration
of 2.1 x 10–4 moles/L.
b)
Calculate the concentration of hydrogen ion, if the pH for a cola is 2.5.
DECIBEL SCALE (Comparing the Intensities of Sounds)
The loudness of any sound is
measured relative to the loudness
of sound at the threshold of hearing.
Sounds at this level are the softest
that can still be heard.
Example 
Sound
soft whisper
normal conversation
shouting
subway
screaming
rock concert
jet engine
space-shuttle launch
Loudness (dB)
30
60
80
90
100
120
140
180
Compare the intensity of the sound of a rock band (120 dB) to the sound of
a normal conversation (60 dB).
I
L  10 log  
 Io 
L is the loudness measured in decibels (dB)
I is the intensity of the sound being measured (W/m2)
Io is the intensity of sound at the threshold of
normal hearing ( Io = 10–12 W/m2 )
Homework: p.499–501 #1 – 4, 5bc, 6bc, 8, 10, 14, 15