Logarithmic Algebra problems

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Algebra

Homework Assignment #4
Due Date: Beginning of Class Wednesday, Feb 15

Chapter 9: Exercise Set 9.3 page 677
Practice problems:
21, 23, 25, 29, 37, 41, 45, 49, 53, 57, 63, 69, 73
Solved Problems
30, 42, 46, 50, 64, 74

Homework Problems

A) –
B) Graph the function and its inverse. What is the domain and

range of f?
C) Write the equation in its equivalent exponential form and then solve for x.

.

Chapter 9: Exercise Set 9.4 page 689
Practice problems:
1, 5, 15, 21, 27, 35, 37, 41, 53, 59, 77, 89, 93
Solved Problems
4, 36, 40, 54, 80, 90, 94, 105

Homework Problems

D) Use the properties of logarithms to expand the expression as much as possible.

E) Use the properties of logarithms to contract the expression as much as possible.

F) Suppose that the formula gives the number of hours

required for a slab of concrete to set where T is the temperature in degrees and D
is the thickness of the slab in inches.

a. Contract the expression to a single log base 2. Hint: Use the change of
base property.

b. Use the change of base property to convert the previous formula so that it
uses base 10, then use a calculator to compute the number of hours needed
to set of slab of concrete that is 10 inches thick if the temperature is 80
degrees.

Chapter 9: Exercise Set 9.5 page 702
Practice problems:
1, 3, 17, 19, 23, 27, 35, 41, 45, 57, 59, 65, 73, 81, 85, 89

Solved Problems
4, 24, 36, 60, 74, 80

Homework Problems

G) Solve the equation
H) Solve the equation . Be sure to reject any solution not in

the domain of the original equation.
Extra Credit

I) Certain atoms are unstable and can decay giving off a particle of radiation. Given
a radioactive sample, about half of the unstable atoms decay in a given period of
time called the half life. The number of unstable atoms remaining in sample is

given by the formula where U is the initial number of unstable

atoms, H is the half life and t is the time.

Suppose that we have two different samples each with a million atoms. Sample A
is Radium 224 which has a half life of 3.66 days. Sample B is Zinc 65 which has
a half life of 243.9 days. Applying the formula to two different times, we can
determine the number of atoms that decay and hence the amount of radiation
emitted in that time frame.

a) For both samples, determine the amount of radiation emitted in the first day.
b) For both samples, determine the amount of radiation emitted in the tenth day.
c) For both samples, determine the amount of radiation emitted in the 100th day.

These values can give us an idea of how dangerous these samples are at different
times after their creation.