Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

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 #42 : Solving And Graphing 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 #43 : Solving And Graphing 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 #3093 : Algebra Ii

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 #3093 : Algebra Ii

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

Example Question #3094 : Algebra Ii

Solve log_2 (x^2 + 7) = 5

Possible Answers:

3, -7

5, -5

4, -6

Correct answer:

5, -5

Explanation:

First, let's change the equation to exponent form:

x^2+7=2^5

Then simplify:

x^2+7=32

And solve:

x^2=25

x=5, x=-5

Both answers are valid because in the original equation is squared, so any negative numbers don't cause the logarithm to become negative.

Report an Error

Example Question #3095 : Algebra Ii

Solve log_6(4x)=log_6(x+9)

Possible Answers:

Correct answer:

Explanation:

We can start by getting both the log terms on the same side of the equation:

log_6(4x)-log_6(x+9)=0

Then we combine log terms:

$log_6(\frac{4x}{x+9})=0\,$

Now we can change to exponent form:

$\frac{4x}{x+9}=6^0$

Anything raised to the th power equals , and from here it becomes a simpler problem to solve:

$\frac{4x}{x+9}=1$

4x=x+9

3x=9

x=3

Report an Error

Example Question #3096 : Algebra Ii

Solve ln(x-2) + ln(x) = ln(2x+9)

Possible Answers:

Correct answer:

Explanation:

First we're going to get all the natural logs on one side of the equation:

ln(x-2) + ln(x) - ln(2x+9)= 0

Next, we're going to combine all the terms into one natural log:

$ln(\frac{(x-2)(x)}{2x+9}) = 0$

Now we can change to exponent form:

$\frac{(x-2)(x)}{2x+9} = e^0$

Anything raised to the th power equals , which helps us simplify:

$\frac{(x-2)(x)}{2x+9} = 1$

(x-2)(x) = 2x+9

x^2-2x = 2x+9

x^2-9=0

From here, we can factor and solve:

(x+3)(x-3)=0

x=3, -3

We have to notice, however, that isn't a valid answer because if we were to plug it into the original formula we would have a negative value in a logarithm.

Report an Error

Example Question #3097 : Algebra Ii

Solve log (3 x + 1) - 2 log (x) = 1 .

Possible Answers:

$-\frac{1}{5}$

$\frac{1}{4}$

$\frac{1}{e}$

$\frac{1}{2}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{2}$

Explanation:

The first thing we can do is write the coefficients in front of the logs as exponents of the terms inside the logs:

log (3 x + 1) - log (x^2) = 1

Next, we combine the logs:

$log(\frac{3x+1}{x^2})=1$

Now we can change the equation into exponent form:

$\frac{(3x+1)}{x^2}=10^1$

When we simplify, we'll also move all the terms to one side of the equation:

10x^2-3x-1=0

From here, we factor to get our solutions:

(5x+1)(2x-1)=0

$x=\frac{1}{2}, -\frac{1}{5}$

The last thing we have to do is check our answers. $\frac{1}{2}$ doesn't raise any problems, but $-\frac{1}{5}$ does. If we plug it back into the original equation, we would be evaluating a negative value in a log, which we can't do.

Report an Error

Example Question #3098 : Algebra Ii

Solve: $2log_{2}(64)-3log_{4}(64)$

Possible Answers:

Correct answer:

Explanation:

In order to solve for the logs, we will need to write the log properties as follows:

x^y = z and $log_{x}z = y$

This means that:

$log_{2}(64) = 6$

$log_{4}(64) = 3$

Replace the values into the expression.

$2log_{2}(64)-3log_{4}(64)= 2(6)-3(3) = 12-9 =3$

The answer is:

Report an Error

Example Question #3099 : Algebra Ii

Solve $ln (e^{5x}) = 2$

Possible Answers:

$\frac{2}{5}$

$\frac{5}{2}$

$\frac{1}{e}$

Correct answer:

$\frac{2}{5}$

Explanation:

First, we rewrite the equation as:

$log_e(e^{5x})=2$

We can use log properties to simplify:

5x=2

From here, simple algebra is used to solve:

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

Report an Error

View Algebra 2 Tutors

Duncan
Certified Tutor

University of Washington-Seattle Campus, Bachelor of Science, Computer Science.

View Algebra 2 Tutors

Soung
Certified Tutor

University of Chicago, Bachelor in Arts, Chemistry. Northwestern University, Doctor of Science, Molecular Pharmacology.

View Algebra 2 Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

All Algebra II Resources

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

Popular Subjects

French Tutors in Atlanta, LSAT Tutors in Dallas Fort Worth, SAT Tutors in Chicago, English Tutors in Chicago, Chemistry Tutors in Denver, Spanish Tutors in Philadelphia, English Tutors in Atlanta, Physics Tutors in Chicago, English Tutors in Phoenix, French Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Boston, GRE Courses & Classes in Denver, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Chicago, SAT Courses & Classes in Atlanta, ACT Courses & Classes in New York City, SAT Courses & Classes in Miami, MCAT Courses & Classes in New York City, MCAT Courses & Classes in Phoenix

Popular Test Prep

MCAT Test Prep in Washington DC, MCAT Test Prep in Boston, ISEE Test Prep in Denver, MCAT Test Prep in Dallas Fort Worth, ACT Test Prep in New York City, GMAT Test Prep in New York City, ACT Test Prep in Phoenix, SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Boston, MCAT Test Prep in Denver

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 : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #42 : Solving And Graphing Logarithms

Example Question #43 : Solving And Graphing Logarithms

Example Question #3093 : Algebra Ii

Example Question #3093 : Algebra Ii

Example Question #3094 : Algebra Ii

Example Question #3095 : Algebra Ii

Example Question #3096 : Algebra Ii

Example Question #3097 : Algebra Ii

Example Question #3098 : Algebra Ii

Example Question #3099 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: