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 I0 is the minimum intensity of sound detectable by the human ear.

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

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

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

Use a scientific calculator to find the log of 0.0038.

Log 0.0038 = -2.420216403

Use a scientific calculator to find the log of 2.6.

Log 2.6 = 0.4150Log 0.00041 = -3.387

Antilogarithm: the inverse of logarithms.

Log 1.2 = 0.4150 Antilogarithms would be

0.4150 = log 1.2

Use a scientific calculator to find the antilog of 0.1790.

10x 0.1790

=1.51

Use a scientific calculator to find the antilog of 0.7210 – 3 .

10x (0.7210 – 3) = 0.00526