MHF4U Unit 6 Log and Exponential Functions.notebook
December 05, 2014
Lesson 6.5
Logarithmic Scales in the Physical Sciences
Learning Goal:
Today I will pose problems based on real-world applications of exponential
and logarithmic functions, and solve these and other such problems by using
a given graph or a graph generated with technology from a table of values or
from its equation.
Catholic Graduate Expectation:
Today I will think reflectively and creatively to evaluate situations and solve
problems.
Logarithmic scales provide a convenient method of comparing values that typically
have a very large range. They are often used in situations in which a variable ranges
over several orders of magnitude, or powers of 10.
Several phenomena in the physical sciences can be described using logarithmic
scales.
The pH Scale: is used to measure the acidity or alkalinity of a chemical solution.
The pH scale is defined as pH = -log[H+], where H+ is the hydronium ion concentration
in a substance, measured in moles per litre.
MHF4U Unit 6 Log and Exponential Functions.notebook
December 05, 2014
Examples:
1. Tomato juice has a hydronium ion concentration of approximately
0.0001mol/L. What is its pH?
pH = -log[H+]
2. Blood has a hydronium ion concentration of approximately 4x10-7mol/L. Determine
its pH. Use the pH scale to determine whether blood is acidic or alkaline.
3. Orange juice has a pH of approximately 3. What is the concentration of hydronium
ions in orange juice?
The Decibel Scale provides a convenient way of comparing sound levels that range
over several orders of magnitude. Each increase of 10 decibels (dB) represents a
tenfold increase in sounds intensity, or loudness.
The difference in sound levels, in decibels,can be found using the equation
where β2-β1 is the difference in sound levels, in decibels and (I2/I1) is the ratio of their
sound intensities, where I is measured in watts per square metre (W/m2)
MHF4U Unit 6 Log and Exponential Functions.notebook
December 05, 2014
Examples:
4. How many times as intense as a whisper is the sound of someone shouting?
5. The sounds level in normal city traffic is approximately 85dB. The sound level while
riding a snowmobile is about 32 times as intense. What is the sound level while riding
a snowmobile, in decibels.
The Richter Scale: The magnitude, M, of
an earthquake is measured using the
Richter scale, which is defined as
M = log ( / o)
where Ι is the intensity of the earthquake
being measured and Ιo is the intensity of a
standard, low-level earthquake.
Examples:
6. how many times as intense as a standard
earthquake is an earthquake measuring 5.2
magnitude on the Richter Scale?
7. What is the magnitude of an earthquake 1 000 000 times are intense as a standard
earthquake?