March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
Get Ready:
A) Expand log
B) Condense log
March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
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March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
Why in the world do we use logarithms?
pH ~ 9.0 Base
Chemistry: Swimming Pool
pH
Acidity level
H+ Hydrogen ion Concentration
pH = -log(H+)
8.4 = -log(0.0000000398)
7.4 = -log(0.00000000398)
pH ~ 5.0 Acid
March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
Why in the world do we use logarithms?
Music: Sounds
I Intensity of a given sound in watts/cm2
I0 Intensity of the softest sound the human ear can hear (10-12 watts/
cm2)
Noise Level in Decibels = 10•log
( )
( )
115 dB = 10•log
I
I0
10-7
10-12
March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
Why in the world do we use logarithms?
Earthquakes: Richter Magnitude Scale
I Intensity of Earthquake in microns
I0 Intensity of a standard Earthquake (10-4 microns)
( )
10
( 10 )
I
Magnitude of Earthquake = log I0
3
7 = log
-4
March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
Richter
Magnitude
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
TNT for Seismic
Energy Yield
-1.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
6
30
320
1
4.6
29
73
1,000
5,100
32,000
80,000
1 million
5 million
32 million
7.5
8.0
8.5
9.0
10.0
12.0
160 million
1 billion
5 billion
32 billion
1 trillion
160 trillion
ounces
pounds
pounds
ton
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
Example
(approximate)
Breaking a rock on a lab table
Large Blast at a Construction Site
Large Quarry or Mine Blast
Small Nuclear Weapon
Average Tornado (total energy)
Little Skull Mtn., NV Quake, 1992
Double Spring Flat, NV Quake, 1994
Northridge, CA Quake, 1994
Hyogo-Ken Nanbu, Japan Quake, 1995;
Largest Thermonuclear Weapon
Landers, CA Quake, 1992
San Francisco, CA Quake, 1906
Anchorage, AK Quake, 1964
Chilean Quake, 1960
(San-Andreas type fault circling Earth)
(Fault Earth in half through center,
OR Earth's daily receipt of solar energy)
March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
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March 01, 2016
Unit: Exp and Logs
Aim: I can develop and use properties of logarithms
Date: 3-1-2016
OCW: Deltamath Log & Expo Practice due Monday
logarithms are the inverse (backwards) exponents
result
log28=3
base
mult. and adding
go together
div. and sub'ing
go together
powers and mult.
go together
exponent
March 01, 2016
March 01, 2016
March 01, 2016