We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Logarithms

Which of the following expressions is equivalent to log(2)^3 ?

Possible Answers:

log(8)

log(2) + 3

log(6)

log(5)

3*log(2)

Correct answer:

3*log(2)

Explanation:

According to the rule for exponents of logarithms, log(a)^b = b*log(a) . As a direct application of this, log(2)^3 = 3*log(2) .

Report an Error

Example Question #11 : Logarithms

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Possible Answers:

4log(2)

3log(2)

8log(2)

log(6)

log(5)

Correct answer:

3log(2)

Explanation:

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log (2^{3})$ .

Then, we use the following rule of logarithms:

$log(m^{n}) = n\cdot log(m)$

Thus, $log(2^{3}) = 3log(2)$ .

Report an Error

Example Question #151 : Algebra Ii

Solve the equation.

$3^{3x-7}=81^{12-3x}$

Possible Answers:

x=33

$x=\frac{11}{3}$

x=11

$x=\frac{22}{3}$

x=9

Correct answer:

$x=\frac{11}{3}$

Explanation:

Change 81 to 3^4 so that both sides have the same base. Once you have the same base, apply log to both sides so that you can set the exponential expressions equal to each other ( 3x-7 = 48-12x ). Thus, $x=\frac{11}{3}$ .

Report an Error

Example Question #1 : Solving And Graphing Logarithmic Equations

Solve the equation.

$36^{10x+2}=(\frac{1}{6})^{13-x}$

Possible Answers:

$x=-\frac{17}{19}$

$x=\frac{17}{19}$

x=19

x=17

$x=\frac{11}{19}$

Correct answer:

$x=-\frac{17}{19}$

Explanation:

Change the left side to 6^2 and the right side to $6^{-1}$ so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other ( 20x+4=-13+x ). $x=-\frac{17}{19}$ .

Report an Error

Example Question #151 : Mathematical Relationships And Basic Graphs

Solve the equation.

$8^{x-1}=(\frac{1}{16})^{4x-3}$

Possible Answers:

x=13

$x=\frac{15}{19}$

x=15

x=30

$x=\frac{11}{19}$

Correct answer:

$x=\frac{15}{19}$

Explanation:

Change the left side to 2^3 and the right side to $2^{-4}$ so that both sides have the same base. Apply log and then set the exponential expressions equal to each other ( 3x-3=-16x+12 ). Thus, $x=\frac{15}{19}$ .

Report an Error

Example Question #1 : Solving Logarithmic Equations

Solve the equation.

$25^{20x+4}=(\frac{1}{125})^{4-3x}$

Possible Answers:

$x=-\frac{20}{31}$

x=18

$x=\frac{20}{31}$

$x=\frac{9}{40}$

$x=-\frac{11}{31}$

Correct answer:

$x=-\frac{20}{31}$

Explanation:

Change the left side to 5^2 and the right side to $5^{-3}$ so that both sides have the same base. Apply log and then set the exponential expressions equal to each other ( 40x+8=-12+9x ). Thus, $x=-\frac{20}{31}$

Report an Error

Example Question #5 : Solving And Graphing Logarithmic Equations

Solve the equation.

$27^{4x-1}=(\frac{1}{3})^{3x+8}$

Possible Answers:

x=1

x=3

$x=\frac{1}{3}$

$x=-\frac{1}{3}$

x=-1

Correct answer:

$x=-\frac{1}{3}$

Explanation:

Change the left side to 3^3 and the right side to $3^{-1}$ so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other ( 12x-3=-3x-8 ). Thus, $x=-\frac{1}{3}$ .

Report an Error

Example Question #11 : Logarithms

Solve for .

$17 + x = \log_{10}10000$

Possible Answers:

10^1^7

983

10^4 - 17

Correct answer:

Explanation:

$log_{10}10000$ can be simplified to since 10^4 = 10000 . This gives the equation:

17 + x = 4

Subtracting from both sides of the equation gives the value for .

$(17 + x) - 17 = (4) - 17 \rightarrow x = -13$

Report an Error

Example Question #152 : Mathematical Relationships And Basic Graphs

Solve the equation.

$5^{3x-9}=25^{^{x+5}$

Possible Answers:

x=21

x=11

x=19

x=5

x=10

Correct answer:

x=19

Explanation:

First, change 25 to 5^2 so that both sides have the same base. Once they have the same base, you can apply log to both sides so that you can set their exponents equal to each other, which yields 3x-9=2x+10 .

x=19

Report an Error

Example Question #8 : Solving And Graphing Logarithmic Equations

Solve the equation.

$7^{3x+4}=49^{x+1}$

Possible Answers:

x=4

x=-2

x=-1

x=2

x=-4

Correct answer:

x=-2

Explanation:

Change 49 to 7^2 so that both sides have the same base so that you can apply log. Then, you can set the exponential expressions equal to each other 3x+4=2x+2 .

Thus, x=-2

Report an Error

View Tutors

Toniann
Certified Tutor

Florida International University, Masters in Education, Curriculum and Instruction.

View Tutors

Krystal
Certified Tutor

Ohio State University-Main Campus, Bachelor of Education, Education. University of Dayton, Masters in Education, Education.

View Tutors

Joanna
Certified Tutor

Texas Christian University, Bachelor of Education, English.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Miami, ISEE Tutors in Dallas Fort Worth, French Tutors in Philadelphia, Computer Science Tutors in Denver, Statistics Tutors in Los Angeles, Math Tutors in San Diego, Biology Tutors in Atlanta, SAT Tutors in Houston, Spanish Tutors in Washington DC, Algebra Tutors in Philadelphia

Popular Courses & Classes

LSAT Courses & Classes in San Diego, SAT Courses & Classes in Denver, Spanish Courses & Classes in Houston, LSAT Courses & Classes in Seattle, SSAT Courses & Classes in New York City, GRE Courses & Classes in Seattle, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in New York City, GRE Courses & Classes in Houston, ACT Courses & Classes in Los Angeles

Popular Test Prep

GRE Test Prep in Denver, GMAT Test Prep in Chicago, SSAT Test Prep in Philadelphia, MCAT Test Prep in New York City, SAT Test Prep in Houston, GMAT Test Prep in Seattle, LSAT Test Prep in Seattle, GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Washington DC, ACT Test Prep in Washington DC

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

High School Math : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : Logarithms

Example Question #11 : Logarithms

Example Question #151 : Algebra Ii

Example Question #1 : Solving And Graphing Logarithmic Equations

Example Question #151 : Mathematical Relationships And Basic Graphs

Example Question #1 : Solving Logarithmic Equations

Example Question #5 : Solving And Graphing Logarithmic Equations

Example Question #11 : Logarithms

Example Question #152 : Mathematical Relationships And Basic Graphs

Example Question #8 : Solving And Graphing Logarithmic Equations

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: