Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Logarithms

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 #38 : Solving Logarithms

Evaluate: $log_{100}10$

Possible Answers:

$\frac{1}{2}$

$\sqrt2$

$\sqrt e$

$\frac{1}{4}$

e^2

Correct answer:

$\frac{1}{2}$

Explanation:

The expression can be rewritten as a fraction.

$log_{100}10 = \frac{log(10)}{log(100)}$

The log based 100 can be rewritten as ten squared.

$\frac{log(10)}{log(100)} = \frac{log(10)}{log(10^2)} = \frac{log(10)}{2log(10)} = \frac{1}{2}$

The answer is: $\frac{1}{2}$

Report an Error

Example Question #421 : Mathematical Relationships And Basic Graphs

Solve the logs: log(2)+log(4)+log(6)-log(8)

Possible Answers:

log(5)

log(4)

3log(2)

log(2)+log(3)

3log(2)+2log(3)

Correct answer:

log(2)+log(3)

Explanation:

For logs that are added, the inner quantities can be multiplied with each other to be combined as a single log.

For logs that are subtracted, the inner quantities would each be divided instead.

Rewrite the expression:

$log(2)+log(4)+log(6)-log(8) =log( \frac{2(4)(6)}{8})$

= log(6)= log(2)+log(3)

The answer is: log(2)+log(3)

Report an Error

Example Question #36 : Solving Logarithms

Evaluate: $log(\frac{x}{10})= 2$

Possible Answers:

$\frac{1}{100}$

1000

$\frac{1}{1000}$

100

$\frac{1}{200}$

Correct answer:

1000

Explanation:

Recall that log has a base of ten.

The equation can be rewritten as:

$log_{10}(\frac{x}{10})= 2$

$log_{10}(x)-log_{10}(10) = 2$

$log_{10}(x)-1= 2$

Add 1 on both sides.

$log_{10}(x)-1+1= 2+1$

$log_{10}(x) = 3$

To eliminate the log based 10 on the left, we will need to raise both terms as exponents of base 10.

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

x=1000

The answer is: 1000

Report an Error

Example Question #182 : Logarithms

Find if $log_{3}(x)=4$ .

Possible Answers:

Correct answer:

Explanation:

First, we start with the full equation:

$log_{3}(x)=4$

Now we can expand the right side of the equation:

$log_{3}(x)=1+1+1+1$

A log of it's own base equals :

$log_{3}(x)=log_{3}(3)+log_{3}(3)+log_{3}(3)+log_{3}(3)$

Now we add the logs on the right side of the equation by multiplying the terms inside the logs:

$log_{3}(x)=log_{3}(3*3*3*3)$

$log_{3}(x)=log_{3}(81)$

x=81

Report an Error

Example Question #183 : Logarithms

Solve $log_{7}(x-4)=0$

Possible Answers:

Correct answer:

Explanation:

By definition, a logarithm of any base that has the term inside is equal to . So we set that term equal to :

x-4=1

x=5

Report an Error

Example Question #181 : Logarithms

Solve $log_{5}(2x)=1$ .

Possible Answers:

$\frac{2}{5}$

$\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

When a logarithm equals , the equation in the logarithm equals the logarithms base:

2x=5

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

Report an Error

Example Question #182 : Logarithms

Solve $log_{10}(x)=-1$

Possible Answers:

Correct answer:

Explanation:

Rearranging the logarithm so that we exchange an exponent for the log we get:

$10^{-1}=x$

x=.1

Report an Error

Example Question #183 : Logarithms

Solve $log_{8}(2x+4)=1$ .

Possible Answers:

$-\frac{3}{2}$

Correct answer:

Explanation:

First we rearrange the equation, trading the logarithm for an exponent:

8^1=2x+4

And then we solve:

4=2x

2=x

Report an Error

Example Question #187 : Logarithms

Solve $log_{3}(x+1)+log_{3}(x)=2$ .

Possible Answers:

Correct answer:

Explanation:

The first thing we can do is combine the log terms:

$log_{3}((x+1)x)=2$

Now we can change to exponent form:

3^2=(x+1)x

We can combine terms and set the equation equal to to have a quadratic equation:

x^2+x-6=0

We then solve the equation and get the answers:

and

can't be an answer, because the values inside a log can't be negative, so that leaves us with a single answer of .

Report an Error

Example Question #188 : Logarithms

Solve log_2 (x + 1) +log_2 (x - 1) = 3 .

Possible Answers:

Correct answer:

Explanation:

The first thing we can do is combine log terms:

log_2((x+1)(x-1))=3

Simplifying the log term gives:

log_2(x^2-1)=3

Now we can change the equation to exponent form:

x^2 - 1 = 2^3

And to solve:

x^2-1=8

x^2=9

x=3, x-3

Here, the solution can't be because the term inside a logarithm can't be negative, so the only solution is .

Report an Error

View Algebra 2 Tutors

Nicholas
Certified Tutor

University of Chicago, Bachelor of Science, Ecology and Evolutionary Biology.

View Algebra 2 Tutors

Dheeraj
Certified Tutor

University of Iowa, Master of Arts, Finance.

View Algebra 2 Tutors

Robert
Certified Tutor

Daytona State College, Bachelor in Arts, Teaching English as a Second Language (ESL).

All Algebra II Resources

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

Popular Subjects

Biology Tutors in Dallas Fort Worth, Computer Science Tutors in New York City, Calculus Tutors in Dallas Fort Worth, SSAT Tutors in Houston, MCAT Tutors in Los Angeles, ISEE Tutors in Denver, Biology Tutors in Phoenix, ACT Tutors in Houston, GMAT Tutors in Houston, Spanish Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Miami, GMAT Courses & Classes in Houston, ACT Courses & Classes in Philadelphia, ISEE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Atlanta, MCAT Courses & Classes in Miami, SAT Courses & Classes in Phoenix, LSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Miami, GRE Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in Philadelphia, GMAT Test Prep in Washington DC, GRE Test Prep in Seattle, MCAT Test Prep in New York City, LSAT Test Prep in Denver, GMAT Test Prep in Seattle, GRE Test Prep in San Diego, GRE Test Prep in Washington DC, MCAT Test Prep in Washington DC, GMAT Test Prep in Houston

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 : Logarithms

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #38 : Solving Logarithms

Example Question #421 : Mathematical Relationships And Basic Graphs

Example Question #36 : Solving Logarithms

Example Question #182 : Logarithms

Example Question #183 : Logarithms

Example Question #181 : Logarithms

Example Question #182 : Logarithms

Example Question #183 : Logarithms

Example Question #187 : Logarithms

Example Question #188 : Logarithms

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: