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 SWBAT:  Translate between logarithms in any base.

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Presentation on theme: " SWBAT:  Translate between logarithms in any base."— Presentation transcript:

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2  SWBAT:  Translate between logarithms in any base

3  One of the more useful logarithms is base 10, because our number system is base 10.  Base 10 logarithms are called Common Logarithms.

4  Measure sound  Chemistry: measures the concentration of hydronium  Telecommunication, electronic: power levels and voltage levels.  Astronomy: the brightness of stars.

5  The loudness L, in decibels, of a particular sound is defined as where I is the intensity of the sound and I 0 is the minimum intensity of sound detectable by the human ear.

6 Decibel s Sounds 120Jet engine / Threshold of Pain 110Pneumatic Drill 100Food Blender 90Moderate Discotheque 80Noisy City Street 70Accounting Office 60Normal Conversations (4 feet) 50Average Residence Area 40City Night Noises 30Broadcast Studio – No program in progress 20Average Whisper (4 feet) 10Rustle of Leaves 0Threshold of Hearing

7  If log 1.2 ≈ 0.0792, find each of the following.  log 120 = log (1.2 * 10 2 ) = log 1.2 + log 10 2 = 0.0792 + 2 = 2.0792 mantissa characteristic

8  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

9  Use a scientific calculator to find the log of 0.0038.  Log 0.0038 = -2.420216403

10  Use a scientific calculator to find the log of 2.6.  Log 2.6 = 0.4150 Log 0.00041 = -3.387

11  Antilogarithm: the inverse of logarithms.  Log 1.2 = 0.4150  Antilogarithms would be 0.4150 = log 1.2

12  Use a scientific calculator to find the antilog of 0.1790.  10 x 0.1790  =1.51

13  Use a scientific calculator to find the antilog of 0.7210 – 3.  10 x (0.7210 – 3)  = 0.00526


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