We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Logarithms

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

← Previous 1 2 3 Next →

Example Question #8 : Simplifying Logarithms

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

Possible Answers:

log(5)

log(2) + 3

log(8)

log(6)

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 #9 : Simplifying Logarithms

Simplify the expression below.

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

Possible Answers:

log(6)

log(5)

3log(2)

8log(2)

4log(2)

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 #1 : Solving And Graphing Logarithmic Equations

Solve the equation.

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

Possible Answers:

x=11

x=33

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

x=9

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

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 #12 : Logarithms

Solve the equation.

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

Possible Answers:

x=17

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

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

x=19

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

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 #13 : Logarithms

Solve the equation.

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

Possible Answers:

x=13

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

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

x=15

x=30

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:

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

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

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

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

x=18

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 #1 : Solving Logarithmic Equations

Solve the equation.

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

Possible Answers:

x=3

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

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

x=-1

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 #12 : Logarithms

Solve for .

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

Possible Answers:

983

10^4 - 17

10^1^7

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 #17 : Logarithms

Solve the equation.

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

Possible Answers:

x=11

x=5

x=21

x=10

x=19

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 #2 : Solving And Graphing Logarithmic Equations

Solve the equation.

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

Possible Answers:

x=-1

x=4

x=-4

x=-2

x=2

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

← Previous 1 2 3 Next →

View Tutors

Basia
Certified Tutor

CUNY Brooklyn College, Bachelor in Arts, Early Childhood Education.

View Tutors

Tessa
Certified Tutor

Western Washington University, Bachelor in Arts, English. Western Washington University, Masters in Education, English.

View Tutors

Laura
Certified Tutor

New York University, Bachelor in Arts, French.

All High School Math Resources

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

Popular Subjects

Physics Tutors in Miami, English Tutors in Houston, Chemistry Tutors in Seattle, Spanish Tutors in Phoenix, Physics Tutors in Boston, Algebra Tutors in New York City, Biology Tutors in Washington DC, Physics Tutors in Atlanta, Physics Tutors in New York City, Math Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in Boston, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in New York City, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in Miami, LSAT Courses & Classes in Denver, MCAT Courses & Classes in New York City, GMAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Miami, Spanish Courses & Classes in New York City

Popular Test Prep

GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Philadelphia, MCAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Houston, LSAT Test Prep in Atlanta, ISEE Test Prep in Seattle, MCAT Test Prep in Atlanta, SSAT Test Prep in Miami, GMAT Test Prep in Chicago, LSAT Test Prep in San Diego

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 : Logarithms

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #8 : Simplifying Logarithms

Example Question #9 : Simplifying Logarithms

Example Question #1 : Solving And Graphing Logarithmic Equations

Example Question #12 : Logarithms

Example Question #13 : Logarithms

Example Question #1 : Solving Logarithmic Equations

Example Question #1 : Solving Logarithmic Equations

Example Question #12 : Logarithms

Example Question #17 : Logarithms

Example Question #2 : 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: