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9.3 Logarithmic Functions (Day 2)

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Recall the graphs of y = log b x: f (x) = log b x has the y-axis as its asymptote The y-axis is x = 0, so if we change the function to f (x) = log b (ax + c), then ax + c = 0 is the asymptote. The x-int is found by letting y = 0 & y-int is when x = 0 Ex 1) Find the asymptote and x- & y-int of h(x) = log (3x + 10) asymptote: 3x + 10 = 0 3x = 10 x-int: 0 = log (3x + 10) 10 0 = 3x + 10 1 = 3x + 10 9 = 3x x = 3 y-int: y = log (3(0) + 10) y = log (10) 10 y = 10 1 y = 1 (3, 0) (0, 1) b > 10 < b < 1

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We can use our calculators to estimate logs we will round to a typical 4 decimal places. Ex 2) Which is wrong? a)log 510 = 2.7076 b) ln 70.5 = 4.2556 c) log 0.03 = 1.5229 Change of Base Formula: typically: which is written as (used in calculus a lot!) Ex 3) Calculate log 2 7 Half Class: both 2.8074

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Logarithms are used to model a wide variety of problems. For example, magnitude of sound, Decibels, is where I = intensity of sound & I 0 is intensity of the threshold of hearing, which is 10 16 W/cm 2 Ex 4) Determine the loudness of each sound to the nearest decibel. a) Whisper: I = 3.16 10 15 b) A subway train: I = 5.01 10 7 Another application is the Richter Scale to measure the magnitude of earthquakes. x 0 is magnitude of zero-level earthquake w/ reading of 0.001 mm x is seismographic reading of quake

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Homework #904 Pg 458 #19 odd, 10, 13, 17, 20, 24, 2729, 3234, 36, 38, 39, 41, 4345