Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Solving Exponential Equations

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 #662 : Exponents

Solve for .

$(7^8)^x=7^{72}$

Possible Answers:

Correct answer:

Explanation:

When dealing with exponents that are raised by another exponent, we multiply the exponents while keeping the base the same.

$(7^8)^x=7^{8x}=7^{72}$ 8x=72 x x=9

Report an Error

Example Question #22 : Solving Exponential Equations

Solve for .

(5^x)^3=125^6

Possible Answers:

Correct answer:

Explanation:

Although we don't have the same bases, we know 125=5^3 . Therefore our equation is $(5^x)^3=(5^3)^6=5^{18}$ . Our equation is now 3x=18 .

x=6

Report an Error

Example Question #23 : Solving Exponential Equations

Solve for .

$9^8\div9^x=9^{-3}$

Possible Answers:

Correct answer:

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

$9^8\div9^x=9^{8-x}=9^{-3}$

8-x=-3

x=11

Report an Error

Example Question #24 : Solving Exponential Equations

Solve for .

$12^x\div12^{20}=12^{2x}$

Possible Answers:

Correct answer:

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

$12^x\div12^{20}=12^{x-20}=12^{2x}$

x-20=2x

x=-20

Report an Error

Example Question #671 : Exponents

Solve for .

$2^x*4^{2x}=2^{60}$

Possible Answers:

Correct answer:

Explanation:

Although the bases are not the same, we know that 4=2^2 . Therefore we now have $2^x*4^{2x}=2^x*(2^2)^{2x}=2^x*2^{4x}=2^{60}$

Now, we can add the exponents. 5x=60

x=12

Report an Error

Example Question #21 : Solving Exponential Equations

Solve for .

4^x+4^x=128

Possible Answers:

Correct answer:

Explanation:

When we add exponents, we try to factor to see if we can simplify it. Let's factor 2^x . We get 4^x(1+1)=4^x*2=128 . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same. Next, we can divide on both sides.

4^x=64 We know 64=4^3

4^x=4^3 With the same base, we know that x=3 .

Report an Error

Example Question #3801 : Algebra Ii

Solve $5^{4x}=125^{12}$ for .

Possible Answers:

$\frac{15}{4}$

$\frac{1}{9}$

Correct answer:

Explanation:

The first step in solving an equation like this to make the base the same on both sides of the equation. Since 5 is a factor of 125, we can rewrite the equation like this:

$5^{4x}=125^{12}$

$5^{4x}=(5^{3})^{12}$

Using the Power of a Power Property of exponents, we get:

$5^{4x}=5^{36}$

If the bases are the same on both sides of the equation, then the exponents must be equal, so

$5^{4x}=5^{36}$ becomes 4x=36

Solving for x:

x=9

Report an Error

Example Question #28 : Solving Exponential Equations

Solve: $5^{3x-6} = 25^{9x-6}$

Possible Answers:

$\frac{2}{5}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{3}{11}$

$\frac{1}{2}$

Correct answer:

$\frac{2}{5}$

Explanation:

In order to solve for the unknown variable, first change the base of the value of 25 to 5^2 .

The equation $5^{3x-6} = 25^{9x-6}$ becomes:

$5^{3x-6} = 5^{2(9x-6)}$

Since the bases are now the same, we can set the powers equal to each other.

3x-6 = 2(9x-6)

Simplify the right side by distributing the integer through the binomial.

3x-6 = 18x-12

Subtract from both sides.

3x-6 -3x= 18x-12-3x

-6= 15x-12

Add twelve on both sides.

-6+12= 15x-12+12

6=15x

Divide by fifteen on both sides and reduce the fraction.

$\frac{6}{15}=\frac{15x}{15}$

$x=\frac{6}{15} = \frac{2}{5}$

The answer is: $\frac{2}{5}$

Report an Error

Example Question #671 : Exponents

Solve: $10^{2x-3} = 1000^{x}$

Possible Answers:

$\textup{The answer is not given.}$

$-\frac{6}{5}$

$-\frac{9}{11}$

Correct answer:

Explanation:

Rewrite the right side of the equation using a base of ten.

1000 = 10^3

One thousand to the power of x can be rewritten using the product of exponents.

$1000^{x} = (10^{3})^x$

$10^{2x-3} = 10^{3x}$

Now that the bases are equal, set the powers equal to each other.

2x-3=3x

Subtract from both sides.

2x-3-2x=3x-2x

Simplify both sides.

-3=x

The answer is:

Report an Error

Example Question #30 : Solving Exponential Equations

Solve the equation: $3^{3x} = 9^{x+3}$

Possible Answers:

$\frac{12}{25}$

$\frac{5}{6}$

$\frac{1}{6}$

Correct answer:

Explanation:

In order to solve this equation, we will need to convert the nine on the right side to a base of three.

9=3^2

Rewrite the equation.

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

Set the powers equal to each other since the bases are common.

3x= 2(x+3)

Distribute the two across the binomial.

3x=2x+6

Subtract from both sides.

3x-2x=2x+6-2x

x=6

The answer is:

Report an Error

View Algebra 2 Tutors

Scott
Certified Tutor

Florida State University, Bachelor of Science, Applied Mathematics. Florida State University, Bachelor of Science, Astrophysi...

View Algebra 2 Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Algebra 2 Tutors

Anne
Certified Tutor

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

All Algebra II Resources

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

Popular Subjects

Math Tutors in Seattle, Statistics Tutors in San Diego, Computer Science Tutors in New York City, Biology Tutors in Seattle, French Tutors in Boston, French Tutors in Seattle, English Tutors in Seattle, GRE Tutors in San Diego, ACT Tutors in San Diego, SAT Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in San Diego, GMAT Courses & Classes in San Diego, SAT Courses & Classes in San Diego, SSAT Courses & Classes in Los Angeles, GRE Courses & Classes in Philadelphia, Spanish Courses & Classes in New York City, SSAT Courses & Classes in Seattle, ISEE Courses & Classes in Miami, LSAT Courses & Classes in Phoenix, ACT Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Washington DC, ISEE Test Prep in Seattle, MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Atlanta, ACT Test Prep in Atlanta, ACT Test Prep in San Diego, ISEE Test Prep in Boston, SAT 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 : Solving Exponential Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #662 : Exponents

Example Question #22 : Solving Exponential Equations

Example Question #23 : Solving Exponential Equations

Example Question #24 : Solving Exponential Equations

Example Question #671 : Exponents

Example Question #21 : Solving Exponential Equations

Example Question #3801 : Algebra Ii

Example Question #28 : Solving Exponential Equations

Example Question #671 : Exponents

Example Question #30 : Solving Exponential Equations

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: