Algebra Answers

10: Which of the following statements are not true?
Check all that apply.

logM^p = p ∙ logM

logM – logN = log(M-N)

logM + logN = log(MN)

log(M/N) = logM/logN


11: Simplify the expression below and write it as a single logarithm:

3log(x+4) – 2log(x-7) + 5log(x-2) – log(x^2)

( (x + 4)^3 (x – 7)^5 )
A: log( ---------------------- )
( (x – 2)^5 x^2 )

( (x + 4)^3 (x – 7)^2 )
B: log( ----------------------- )
( (x – 2)^-5 x^-2 )

( x^2 (x + 4)^3 (x – 7)^5 )
C: log( ---------------------------- )
( (x – 2)^5 )

( (x + 4)^3 (x – 2)^5 )
D: log( ----------------------- )
( (x – 7)^2 x^2 )


12: If log75 = 1.875 , then what is the value of log10075

A: 0.1875
B: 0.9375
C: .01875
D: .009375

6: Which of the following functions have a domain of (-∞,∞) and a range of (2,∞)
Check all that apply.

f(x) = 0.25^x -2
f(x) = 3^x -2
f(x) = 0.25^x + 2
f(x) = 3^x + 2

7: What is the sum of the first five terms of the geometric sequence in which a1 = 3 and r = 1/3?
Express your answer as an improper fraction using the slash(/) key and no spaces._______


8: The original purchase price of a car is $12,000. Each year, its value depreciates by 5%. Three years after the purchase, what is the value of the car?

A: $1.50
B: $13,891.50
C: $10,830
D: $10,288.50


9: Which of the following sequences are geometric?
Check all that apply

6,18,54,162,486

2,5,8,11,14,17

-4,-2,-1,-0.5,-0.25,-0.125

2,3,5,8,13,21

1: Which of the following pairs are equivalent statements?

A: logbN = p and B^p = N

B: N^1/b = p and b^p = N

C: logNb = p and B^p = N

D: logpN = b and b^p = N


2: Which of the following statements are true?
Check all that apply.

The graph of f(x) = ½ 3√x looks like the graph of f(x) = 3√x , but will shrink it horizontally by a factor of ½

f(x) = ½ √x has the same domain and range as f(x) = 3√x

The graph of f(x) = ½ 3√x looks like the graph of f(x) = 3√x , but will shrink vertically by a factor of ½

The graph of f(x) = ½ √x does not look like the graph of f(x) = 3√x because the roots are different.


3: Simplify the expression shown below:
(a^2 b^5 c^3)^4 (a^3 b^3)^3 (a^2 c)^2

A: a^21 b^24 c^10

B: a^13 b^19 c^13

C: a^21 b^29 c^14

D: 6(a^8 b^12 c^4)

13: The number of people in town of 10,000 who have heard a rumor stated by a small group of people is given by the following function:

10,000
N(t) = ------------------
5 + 1245e^-.97t

How many people were in the group that started the rumor?:
How many people have heard the rumor after 1 day?:
How many people have heard the rumor after 5 days?:
How long will it be until 1,000 of the people in the town have heard the rumor?:

: A lake is stocked with 1,500 young trout. If the number of the original trout alive after x years is given by the function P(x) = 1,500 e^-0.4x , When will there be 300 of the original trout left.?

: A hot bowl of soup cools accordingly to Newton's law of cooling. Its temperature (in degrees Fahrenheit) at time t is given by T(t) = 68 + 144e^-.04t , where t is given in minutes.

What was the initial temperature of the soup?:
What was the temperature of the soup after 15 minutes?:
How long after serving is the soup 125 Degrees F?:

6: If log55 = 1.74 , what is the value, of logsub1000^55?


A: 0..05801
B: 0.00174
C: 0.5801
D: 0.0174


7: Let logbA = 1; logbC = 3; logbD = 4

What is the value of logb(A^5C^2/D^6)

A: 26
B: -13
C: 0
D: There is not enough information to answer the question.

8: If logM/N = 4 and logP/N = 7 , what can you say about the relationship between M and P?

A: P = 1000M
B: P = 100M
C: P = 3M
D: M = 3P


9: Solve the following equation for x:
logx + log(x+2) = log(3x)

A: There are no solutions
B: x = 0
C: x = 0, 1
D: x = 1


10: Complete the sentence below:

In 25 is the power to which _____ must be raised in order to produce a value of 25._____

8: How many times more intense is an earthquake that measures 7.5 on the Richter scale than one that measures 6.7? (Recall that the Richter scale defines magnitude of an earthquake with the equation M = logI/S, where I is the intensity of the earthquake being measured, and S is the intensity of a standard earthquake.)

9: The nth term of a geometric sequence is given by a sub n = 27(0.1)^n-1. Write the first 5 terms and find the 10th partial sum.

First five terms: ___ ___ ___ ___ ___
10th partial sum: _________


10: A basketball is dropped from an original height of 9 feet and on each bounce, bounces up 2/3 the distance it fell. How far will it have traveled by the time it hits the ground the 4th time?

1: Which of the following are true statements?
Check all that apply

log(M/N) = logM – logN

logM^p = p ∙ logM

(logM)^p = p ∙ logM

log(M/N) = logM/logN


2: Fill in the blank: log sub 5 625 = ______∙ _________


3: Which of the following equations is equivalent to b^v = x ?

A: y = Inx
B: y = logb X
C: y = logb Y
D: y = logX

4: Rewrite the following expression as a single logarithm:

(2log(x + 3) + 2log(x – 2)) – (3log(x – 7) + log (x^2))

( (x+3)^2 (x-7)^3 )
A: log (---------------------)
( (x-2)^-5 x^-2 )

( (x+3)^2 (x-2)^2 )
B: log ( --------------------)
( (x-7)^3 x^2 )


( (x+3)^2 (x-7)^3) )
C: log ( -------------------- )
( x^2(x-2)^5 )


( x^2 (x+3)^2 (x-7)^3 )
D: log ( ----------------------- )
( x^2 (x-2)^5 )


5: If logx = -5, what is x?
A: 0.00001
B: -0.00001
C: -0.00005
D: 0.00005

1: Describe the domain and range and sketch the graph.

5
f(x) = √(x-4) + 2 The five is in between the area above it rests.

2: Describe the domain and range and sketch the graph. f(x) = e^(x-2) + 3

3: Describe the domain and range and sketch the graph. f(x) = (1/2)^x - 3


4: Describe the domain and range and sketch the graph. f(x) = log(x+1) – 2


5: Solve each equation for x. Show work 5 = log sub 3 (x^2 + 18)

6: Solve each equation for x. Show work -2 = log(3x + 5)

7: Solve each equation for x. Show work e^x e^(x+1) = 1

5: The function Q(t) = Qoe^-kt may be used to model radioactive decay. Q represents the quantity remaining after t years; k is the decay constant, 0.00011. How long, in years, will it take for a quantity of plutonium-240 to decay to 25% of its original amount?

A: 12,602 years
B: 1,575 Years
C: 3,150 years
D: 9,450 years


6: Plutonium-240 decays according to the function Q(t)= Qoe^-kt . How long will it take 27 grams of plutonium-240 to decay to 9 grams?

K is the decay constant, 0.00011

A: 2,100 years
B: 1.44 years
C: 18,900 years
D: 9,987 years