 SWBAT:  Translate between logarithms in any base

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

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

 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.

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

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

 If log 1.2 ≈ , find each of the logarithms.  Log 0.12  Log 0.12 ≈ log (1.2 * )  = Log log  = – 1  = –

 Use a scientific calculator to find the log of  Log =

 Use a scientific calculator to find the log of 2.6.  Log 2.6 = Log =

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

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

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