Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3871 : Algebra Ii

Solve: $2^{3x+3} = 8^{-5x}$

Possible Answers:

$-\frac{2}{7}$

$-\frac{1}{6}$

$\frac{2}{3}$

Correct answer:

$-\frac{1}{6}$

Explanation:

Change the base of the second term to base two.

8=2^3

$2^{3x+3} =(2^3)^{-5x}$

Simplify the right side by multiplying the exponents.

$2^{3x+3} =(2)^{-15x}$

Now that the bases are common, the exponents can be set equal to each other.

3x+3 = -15x

Subtract from both sides.

3x+3-3x = -15x-3x

3=-18x

Divide by negative 18 on both sides.

$\frac{3}{-18}=\frac{-18x}{-18}$

The answer is: $-\frac{1}{6}$

Report an Error

Example Question #91 : Solving Exponential Equations

Solve: $4^6 = 2^{3x-3}$

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{5}$

Correct answer:

Explanation:

To evaluate this equation, we will need to change the base of the left side.

4=2^2

Rewrite the equation.

$(2^2)^6 = 2^{3x-3}$

$2^{12}= 2^{3x-3}$

Now that both bases are similar, we can set the exponents equal to each other.

12=3x-3

Add 3 on both sides.

12+3=3x-3+3

15=3x

Divide by three on both sides.

The answer is:

Report an Error

Example Question #101 : Solving And Graphing Exponential Equations

Solve the equation: $2(\frac{1}{2})^{7x-1}= (\frac{1}{4})^{3x+2}$

Possible Answers:

$\frac{2}{3}$

$\frac{1}{6}$

$\textup{There is no solution.}$

Correct answer:

Explanation:

Rewrite both sides of the equation so that we have same bases.

$2(\frac{1}{2})^{7x-1}= (\frac{1}{4})^{3x+2}$

2=2^1

$\frac{1}{2} = 2^{-1}$

$\frac{1}{4} = 2^{-2}$

$2^1\cdot (2^{-1})^{7x-1}= (2^{-2})^{3x+2}$

Simplify the exponents.

$2^1\cdot (2^{-7x+1})= 2^{-6x-4}$

Add the exponents on the left side.

$2^{-7x+2}= 2^{-6x-4}$

Now that both sides have same bases, we can set the exponential terms equal.

-7x+2 = -6x-4

Add on both sides.

-7x+2+7x = -6x-4+7x

2 = x-4

Add four on both sides.

2 +4= x-4+4

The answer is:

Report an Error

Example Question #98 : Solving Exponential Equations

Solve: $3^4 = (\frac{1}{27})^{9x-3}$

Possible Answers:

$-\frac{2}{3}$

$\frac{1}{9}$

$\frac{5}{27}$

$-\frac{13}{27}$

$\frac{5}{3}$

Correct answer:

$\frac{5}{27}$

Explanation:

In order to solve this, we will need to rewrite the fractional base to base three.

$\frac{1}{27} = 3^{-3}$

Rewrite the equation using this base.

$3^4 = (3^{-3})^{9x-3}$

Now that both bases are common, we can set up an equation where the powers are equal.

4=-3(9x-3)

Use distribution to simplify the right side.

4=-27x+9

Subtract nine from both sides.

4-9=-27x+9-9

-5 = -27x

Divide by negative 27 on both sides.

$\frac{-5 }{-27}= \frac{-27x}{-27}$

The answer is: $\frac{5}{27}$

Report an Error

Example Question #1211 : Mathematical Relationships And Basic Graphs

Evaluate: $(\frac{2}{3})^{3x-8} =( \frac{8}{27})^{-x-2}$

Possible Answers:

$-\frac{5}{3}$

$\frac{1}{3}$

$-\frac{1}{4}$

$\frac{7}{3}$

$\frac{2}{9}$

Correct answer:

$\frac{1}{3}$

Explanation:

To solve this exponential equation, we will need to change the base of the second term. Notice that both the numerator and denominator are the values of the left fraction cubed.

$\frac{8}{27} = (\frac{2}{3})^3$

Rewrite the equation.

$(\frac{2}{3})^{3x-8} =( \frac{2}{3})^{3(-x-2)}$

With common bases, we can set the exponents equal to each other.

3x-8 = 3(-x-2)

Distribute the right side.

3x-8 = -3x-6

Add on both sides.

3x-8 +(3x)= -3x-6+(3x)

6x-8 = -6

Add 8 on both sides.

6x-8 +8= -6+8

6x=2

Divide by six on both sides.

$\frac{6x}{6}=\frac{2}{6}$

The answer is: $\frac{1}{3}$

Report an Error

Example Question #100 : Solving Exponential Equations

Solve: $(\frac{1}{9}) ^{81} = 3^{2x-10}$

Possible Answers:

$\textup{No solution.}$

Correct answer:

Explanation:

In order to solve this equation, we will need to change the base of the left side.

Rewrite one-ninth as base three.

$\frac{1}{9} = 3^{-2}$

Rewrite the equation.

$(3^{-2}) ^{81} = 3^{2x-10}$

Now that both bases are common, we can set both powers equal.

(-2)(81) = 2x-10

Simplify the left side and solve for x.

-162 = 2x-10

Add 10 on both sides, and then divide by two.

-162 +10= 2x-10+10

$\frac{-152}{2}=\frac{2x}{2}$

The answer is:

Report an Error

Example Question #101 : Solving Exponential Equations

Solve: $2^{5x+2} = (\frac{1}{2})^{10x+3}$

Possible Answers:

$\frac{1}{15}$

$\frac{1}{12}$

$-\frac{1}{6}$

$-\frac{1}{3}$

$-\frac{1}{9}$

Correct answer:

$-\frac{1}{3}$

Explanation:

Change the base of the right side.

$\frac{1}{2} =2^{-1}$

Rewrite the base of the right side.

$2^{5x+2} = (2^{-1})^{10x+3}$

Set the exponents equal to each other now that both of the bases are alike.

5x+2 = -1(10x+3)

Simplify both sides.

5x+2 = -10x-3

Add 10x on both sides.

5x+2 +10x= -10x-3+10x

15x+2= -3

Subtract two on both sides.

15x+2-2= -3-2

15x=-5

Divide by 15 on both sides.

$\frac{15x}{15}=\frac{-5}{15}$

Reduce both fractions.

The answer is: $-\frac{1}{3}$

Report an Error

Example Question #102 : Solving Exponential Equations

Solve the equation: $8^{10x} = 8^{-9x-19}$

Possible Answers:

$\textup{There is no solution.}$

$\frac{19}{8}$

Correct answer:

Explanation:

The bases on both sides of the equation are equal. This means we can set the powers equal to each other.

10x= -9x-19

Add on both sides.

10x+9x= -9x-19+9x

19x = -19

Divide by 19 on both sides.

$\frac{19x}{19} = \frac{-19}{19}$

The answer is:

Report an Error

Example Question #101 : Solving Exponential Equations

Solve the equation: $4^{3x+2} = (\frac{1}{4})^{-9x+3}$

Possible Answers:

$-\frac{5}{12}$

$\textup{No solution.}$

$\frac{5}{12}$

$\frac{5}{3}$

$\frac{5}{6}$

Correct answer:

$\frac{5}{6}$

Explanation:

Change the base on the right side to match the left side.

$\frac{1}{4} = 4^{-1}$

$4^{3x+2} = (4)^{-1(-9x+3)}$

Set the exponents equal to each other since both bases are equal.

3x+2 = -1(-9x+3)

Simplify both sides.

3x+2 =9x-3

Subtract both sides by and add both sides by three.

3x+2 -(3x)+[3]=9x-3-(3x)+[3]

5=6x

Divide both sides by six.

$\frac{5}{6}=\frac{6x}{6}$

The answer is: $\frac{5}{6}$

Report an Error

Example Question #111 : Solving And Graphing Exponential Equations

Solve: $16^{26} = 8^{3x+3}$

Possible Answers:

$\frac{95}{9}$

$\textup{The answer cannot be determined.}$

$\frac{17}{3}$

$\frac{35}{9}$

$\frac{35}{3}$

Correct answer:

$\frac{95}{9}$

Explanation:

In order to solve the equation, we will need to change the bases of both sides.

16= 2^4

8=2^3

Rewrite the equation using these two bases.

$(2^4)^{26} =(2^3)^{3x+3}$

Now that both sides have equal bases, we can set the exponents alike.

4(26) = 3(3x+3)

Simplify both sides.

104 = 9x+9

Subtract nine from both sides, and then divide both sides by nine.

104-9 = 9x+9-9

95=9x

$\frac{95}{9}=\frac{9x}{9}$

The answer is: $\frac{95}{9}$

Report an Error

View Algebra 2 Tutors

Sahibzada
Certified Tutor

Northwestern University, Bachelor of Science, Materials Engineering.

View Algebra 2 Tutors

Anne
Certified Tutor

University of Maryland-Baltimore, Doctor of Science, Accounting.

View Algebra 2 Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Phoenix, English Tutors in Atlanta, SAT Tutors in Houston, SSAT Tutors in Chicago, ACT Tutors in Dallas Fort Worth, Math Tutors in Philadelphia, SAT Tutors in Phoenix, French Tutors in Seattle, Algebra Tutors in Houston, Spanish Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in Washington DC, Spanish Courses & Classes in Boston, GRE Courses & Classes in Miami, SSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Miami, LSAT Courses & Classes in Boston, ACT Courses & Classes in Denver, SAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Phoenix, ISEE Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Phoenix, MCAT Test Prep in New York City, GMAT Test Prep in Los Angeles, ISEE Test Prep in New York City, SSAT Test Prep in Denver, LSAT Test Prep in Seattle, SSAT Test Prep in Chicago, ACT Test Prep in Atlanta

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3871 : Algebra Ii

Example Question #91 : Solving Exponential Equations

Example Question #101 : Solving And Graphing Exponential Equations

Example Question #98 : Solving Exponential Equations

Example Question #1211 : Mathematical Relationships And Basic Graphs

Example Question #100 : Solving Exponential Equations

Example Question #101 : Solving Exponential Equations

Example Question #102 : Solving Exponential Equations

Example Question #101 : Solving Exponential Equations

Example Question #111 : Solving And Graphing Exponential Equations

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: