swbat: translate between logarithms in any base
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SWBAT:Translate between logarithms in any base
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One of the more useful logarithms is base 10, because our number system is base 10.
Base 10 logarithms are called Common Logarithms.
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Measure sound Chemistry: measures the
concentration of hydronium
Telecommunication, electronic: power levels and voltage levels.
Astronomy: the brightness of stars.
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The loudness L, in decibels, of a particular sound is defined as
where I is the intensity of the sound and I0 is the minimum intensity of sound detectable by the human ear.
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Decibels
Sounds
120 Jet engine / Threshold of Pain
110 Pneumatic Drill
100 Food Blender
90 Moderate Discotheque
80 Noisy City Street
70 Accounting Office
60 Normal Conversations (4 feet)
50 Average Residence Area
40 City Night Noises
30 Broadcast Studio – No program in progress
20 Average Whisper (4 feet)
10 Rustle of Leaves
0 Threshold of Hearing
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If log 1.2 ≈ 0.0792, find each of the following.
log 120 = log (1.2 * 102)= log 1.2 + log 102 = 0.0792 + 2 =
2.0792
mantissa characteristic
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If log 1.2 ≈ 0.07920, find each of the logarithms.
Log 0.12 Log 0.12 ≈ log (1.2 * 10-1) = Log 1.2 + log 10 -1 = 0.0792 + – 1 = – 0.9208
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Use a scientific calculator to find the log of 0.0038.
Log 0.0038 = -2.420216403
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Use a scientific calculator to find the log of 2.6.
Log 2.6 = 0.4150Log 0.00041 = -3.387
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Antilogarithm: the inverse of logarithms.
Log 1.2 = 0.4150 Antilogarithms would be
0.4150 = log 1.2
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Use a scientific calculator to find the antilog of 0.1790.
10x 0.1790
=1.51
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Use a scientific calculator to find the antilog of 0.7210 – 3 .
10x (0.7210 – 3) = 0.00526