We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Exponential Ratios and Rational Numbers

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #114 : Exponents

If and are positive integers and , then what is the value of $\frac{m}{n}$ ?

Possible Answers:

$\frac{1}{3}$

$\frac{1}{16}$

$\frac{5}{3}$

Correct answer:

Explanation:

4³= 64

Alternatively written, this is 4(4)(4) = 64 or 4³= 64^1.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

Report an Error

Example Question #115 : Exponents

Write the following logarithm in expanded form:

$\log x^{2}y$

Possible Answers:

$2\left ( \log xy \right )$

$\log x+\log y$

$2\log x+\log y$

$\log x^{2}+\log y$

$2\log x-\log y$

Correct answer:

$2\log x+\log y$

Explanation:

$\log x^{2}y=\log x^{2}+\log y=2\log x+\log y$

Report an Error

Example Question #10 : Exponents And Rational Numbers

Com_exp_1

Which of the following lists the above quantities from least to greatest?

Possible Answers:

I, IV, III, II

II, III, I, IV

I, IV, II, III

IV, III, II, I

I, III, II, IV

Correct answer:

I, III, II, IV

Explanation:

Com_exp_2

Com_exp_3

Report an Error

Example Question #1 : Exponents And Rational Numbers

Solve for .

$2^{x}= 64$

Possible Answers:

x=6

x=-6

x=5

$x=64^{2}$

x=64

Correct answer:

x=6

Explanation:

Since $2^{x}= 2^{6}$

Hence x=6

Report an Error

Example Question #2 : Exponents And Rational Numbers

Simplify:

$\sqrt[3]{x^{10}y^{8}z^{9}}$

Possible Answers:

$x^{3}y^{2}z^{3}^{\sqrt[3]{xyz}}$

$x^{3}y^{3}z^{3}$

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

$\sqrt[3]{xy^{2}}$

$x^{3}y^{2}z^{3}$

Correct answer:

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

Explanation:

$\sqrt[3]{x^{9}xy^{6}y^{2}z^{9}}=x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

Report an Error

Example Question #3 : Exponents And Rational Numbers

Solve for :

$\sqrt{x} -1= 4$

Possible Answers:

Correct answer:

Explanation:

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

Report an Error

Example Question #4 : Exponents And Rational Numbers

Evaluate:

$\log 0.1=$

Possible Answers:

$\frac{1}{10}$

Correct answer:

Explanation:

$0.1= 10^{-1}$

$\log 0.1=-1$

Report an Error

Example Question #1 : Exponents And Rational Numbers

Solve for .

$\log_{2}x=4$

Possible Answers:

Correct answer:

Explanation:

$x= 2^4{}= 16$

Report an Error

Example Question #2 : Exponents And Rational Numbers

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

Possible Answers:

a+b

$b^{2}$

$a^{2}$

Correct answer:

a+b

Explanation:

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is a+b .

Report an Error

Example Question #3 : Exponents And Rational Numbers

Solve for .

$\log (x+3)+\log x=1$

Possible Answers:

$-5\ or\ 2$

$5\ or\ -2$

Correct answer:

Explanation:

Use the rules of logarithms to combine terms.

$\log (x(x+3))=1$

Hence, $x(x+3)=10^{1}$

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

x^2+3x-10=0

By fatoring we get (x+5)(x-2)=0

Hence $x=-5\ or\ 2$ .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

Report an Error

View PSAT Mathematics Tutors

Shakeel
Certified Tutor

View PSAT Mathematics Tutors

Evgenii
Certified Tutor

View PSAT Mathematics Tutors

Ayan
Certified Tutor

Vellore Institute of Technology, Bachelor, Chemical Engineering. University of Calgary, Master's/Graduate, Chemical and Petro...

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Miami, MCAT Tutors in Seattle, Spanish Tutors in Chicago, SSAT Tutors in Chicago, Calculus Tutors in Miami, SSAT Tutors in Houston, Calculus Tutors in Los Angeles, GRE Tutors in Chicago, GMAT Tutors in San Diego, Chemistry Tutors in Denver

Popular Courses & Classes

GRE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Boston, SSAT Courses & Classes in Boston, ISEE Courses & Classes in Houston, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Denver, LSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Denver, SSAT Courses & Classes in Phoenix, SAT Courses & Classes in Atlanta

Popular Test Prep

SSAT Test Prep in San Diego, MCAT Test Prep in Los Angeles, GRE Test Prep in Atlanta, ISEE Test Prep in Miami, ISEE Test Prep in Boston, MCAT Test Prep in Phoenix, LSAT Test Prep in Atlanta, ISEE Test Prep in Houston, LSAT Test Prep in Houston, MCAT 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

PSAT Math : Exponential Ratios and Rational Numbers

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #114 : Exponents

Example Question #115 : Exponents

Example Question #10 : Exponents And Rational Numbers

Example Question #1 : Exponents And Rational Numbers

Example Question #2 : Exponents And Rational Numbers

Example Question #3 : Exponents And Rational Numbers

Example Question #4 : Exponents And Rational Numbers

Example Question #1 : Exponents And Rational Numbers

Example Question #2 : Exponents And Rational Numbers

Example Question #3 : Exponents And Rational Numbers

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: