Homework

9.3 Logarithmic Functions (Day 2) 1Recall the graphs of y = logb x:

f (x) = logb x has the y-axis as its asymptote The y-axis is x = 0, so if we change the function to f (x) = logb (ax + c), then ax + c = 0 is the asymptote. The x-int is found by letting y = 0 & y-int is when x = 0Ex 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)100 = 3x + 10 1 = 3x + 10 9 = 3x x = 3 y-int: y = log (3(0) + 10) y = log (10) 10y = 101 y = 1(3, 0)(0, 1)b > 10 < b < 1We can use our calculators to estimate logs we will round to a typical 4 decimal places.

Ex 2) Which is wrong?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 log2 7Half Class: Half Class:

both 2.8074

Logarithms are used to model a wide variety of problems.For example, magnitude of sound, Decibels, iswhere I = intensity of sound & I0 is intensity of the threshold of hearing, which is 1016 W/cm2

Ex 4) Determine the loudness of each sound to the nearest decibel. a) Whisper: I = 3.16 1015

b) A subway train: I = 5.01 107

Another application is the Richter Scale to measure the magnitude of earthquakes.

x0 is magnitude of zero-level earthquake w/ reading of 0.001 mmx is seismographic reading of quakeHomework#904 Pg 458 #19 odd, 10, 13, 17, 20, 24, 2729, 3234, 36, 38, 39, 41, 4345