Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Solving Exponential Equations

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 Next →

Example Question #21 : Solving Exponential Equations

Solve for :

$2^{x+1}=8^4$

Possible Answers:

x=-7

x=4

x=-11

x=11

Correct answer:

x=11

Explanation:

Step 1: Rewrite the right side as a power of :

$8^4=8\cdot8\cdot8\cdot8$

8=2^3

$8^4=2^3\cdot2^3\cdot2^3\cdot2^3$

$8^4=2^{3+3+3+3}=2^{3\cdot 4}=2^{12}$

Step 2: Rewrite the original equation:

$2^{x+1}=2^{12}$

Step 3: Since the bases are equal, I can set the exponents equal.

So, $x+1=12\implies x=11$

Report an Error

Example Question #341 : Gre Subject Test: Math

Solve for :

$2^{x+3}=8^4$

Possible Answers:

Correct answer:

Explanation:

Rewrite the right hand side such that it has the same base as the expression on the right hand side.

$8^4=\big(2^3\big)^{4}$
Apply the rule of stacked exponents. We multiply the exponents together and keep the same base:

$\large \big(2^3\big)^4=2^{3\cdot4}=2^{12}$

Now that we have rewrote the right hand side in the same way as the left, we can equate them:

$\large 2^{x+3}=2^{12}$

Now that we have the same bases, we can equal the exponents and solve for x...

$\large x+3=12 \implies x=9$

Report an Error

Example Question #21 : Solving Exponential Equations

Find the value that makes the statement $(36)^{x+2}=6$ true.

Possible Answers:

$\frac {1}{2}$

$\frac {3}{2}$

$-\frac {3}{2}$

Correct answer:

$-\frac {3}{2}$

Explanation:

Step 1: Re-write the left side so we have the same base as the right side...

$(36)^{x+2}=6\implies (6^2)^{x+2}=6^1$

Step 2: Multiply the stacked exponents on the left hand side...

We will apply the rule: $(a^b)^c=a^{b\cdot c}$

So, $(6^2)^{x+2}=6^{2(x+2)}=6^{2x+4}$

Step 3: We can now set the exponents equal to each other, since we have the same base.

2x+4=1

2x=1-4

2x=-3

$\frac {{\color{Blue} 2}x}{{\color{Blue} 2}}=-\frac {{\color{Red} 3}}{{\color{Blue} 2}}$

$x=-\frac {3}{2}$

Report an Error

Example Question #21 : Solving Exponential Equations

Find one possible value of , given the following equation:

$343=7^{15t-12}$

Possible Answers:

Cannot be determined from the information given.

t=1

t=5

t=0

t=-3

Correct answer:

t=1

Explanation:

We begin with the following:

$343=7^{15t-12}$

This can be rewritten as

$7^3=7^{15t-12}$

Recall that if you have two exponents with equal bases, you can simply set the exponents equal to eachother. Do so to get the following:

3=15t-12

Solve this to get t.

15=15t

t=1

Report an Error

← Previous 1 2 3 Next →

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Max
Certified Tutor

SHAHiDBEHESHTiUNiVERSiTY, Bachelor of Science, Mathematics. SHAHiDBEHESHTiUNiVERSiTY, Master of Science, Mathematics.

View Tutors

Swagatika
Certified Tutor

Regional Institute of Education Bhubaneswar, Bachelor of Economics, Mathematics.

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Denver, Reading Tutors in Atlanta, Algebra Tutors in Chicago, Computer Science Tutors in Los Angeles, ISEE Tutors in San Francisco-Bay Area, Chemistry Tutors in Phoenix, Computer Science Tutors in Phoenix, Calculus Tutors in Boston, Statistics Tutors in Boston, GMAT Tutors in Houston

Popular Courses & Classes

SSAT Courses & Classes in Atlanta, SAT Courses & Classes in Seattle, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Washington DC, SAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Denver, Spanish Courses & Classes in Miami, GRE Courses & Classes in Washington DC, GMAT Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in Seattle, SAT Test Prep in Miami, GMAT Test Prep in Washington DC, GMAT Test Prep in Miami, ISEE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Denver, GMAT Test Prep in Los Angeles, ISEE Test Prep in Boston, LSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in San Francisco-Bay Area

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

GRE Subject Test: Math : Solving Exponential Equations

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #21 : Solving Exponential Equations

Example Question #341 : Gre Subject Test: Math

Example Question #21 : Solving Exponential Equations

Example Question #21 : Solving Exponential Equations

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: