# 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.