Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Solving and Graphing 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 #71 : Solving And Graphing Logarithms

Solve 2 log( x) = log (9 )+ log (8) - log (18) .

Possible Answers:

$\pm2$

Correct answer:

Explanation:

The first thing we can do is combine all the log terms on the right side of the equation:

$2log(x)=log(\frac{9*8}{18})$

Next, we can take the coefficient from the left term and make it an exponent:

log(x^2)=log(4)

Now we can cancel the logs from both sides:

x^2=4

$x=\pm2$

When we put back into the original question, we don't have problems. When we try it with however, we get errors, so that's not a valid answer:

x=2

Report an Error

Example Question #72 : Solving Logarithms

Solve 3 log (x) = log (64) .

Possible Answers:

Correct answer:

Explanation:

First, we take the coefficient, , and make it an exponent:

log (x^3) = log (64)

Now we can cancel the logs:

x^3=64

$x=\pm4$

When we check our answers, however, we notice that results in errors, so that's not a valid answer:

x=4

Report an Error

Example Question #211 : Logarithms

Solve log_3 (x) + log_3(x - 7) = log_3 (8) ,

Possible Answers:

Correct answer:

Explanation:

First, we combine the log terms on the left of the equation:

log_3 ((x)(x-7)) = log_3 (8)

Now we can cancel the logs on each side:

x^2-7x=8

We can subtract from each side to set the equation equal to . this will give us a nice quadratic equation to solve:

x^2-7x-8=0

(x-8)(x+1)=0

x=8, -1

Notice that is not a valid answer, because if we plug it into the original equation then we would be taking the log of a negative number, which we can't do. Our only solution is:

x=8

Report an Error

Example Question #74 : Solving Logarithms

Solve log_2(x-4) = 3-log_2 (x+3) /

Possible Answers:

Correct answer:

Explanation:

The first thing we can do is move both log functions to one side of the equation:

log_2(x-4) + log_2 (x+3)= 3

Then we can combine the log functions (remember, when you add logs, we multiply the terms inside):

log_2((x-4)(x+3))= 3

Now we can rewrite the equation in exponent form (and FOIL the multiplied terms):

x^2-x-12=2^3

We can collect all the terms on one side of the equation, and then solve the quadratic:

x^2-x-20=0

(x-5)(x+4)=0

x=-4, 5

However, if we plug into the initial equation, we would be taking the log of a negative number, which we can't do, so it's not a valid solution:

x=5

Report an Error

Example Question #75 : Solving Logarithms

Solve log_7(6x-16)=log_7(x-1) .

Possible Answers:

Correct answer:

Explanation:

We first put both logs on one side of the equation:

log_7(6x-16)-log_7(x-1)=0

Now we combine the log terms (remember, when we subtract logs we divide the terms inside):

$log_7(\frac{(6x-16)}{(x-1)})=0$

We can now rewrite the equation in exponential form:

$\frac{6x-16}{x-1}=7^0$

Anything raised to the power is , and now we can solve algebraically:

6x-16=x-1

5x=15

x=3

Report an Error

Example Question #76 : Solving Logarithms

Solve log_5(3x-8)=2 .

Possible Answers:

Correct answer:

Explanation:

We start by rewriting the equation in exponential form:

3x-8=5^2

Now we can simplify:

3x-8=25

3x=33

x=11

Report an Error

Example Question #211 : Logarithms

Solve log (2x) = log (24) .

Possible Answers:

Correct answer:

Explanation:

We can either do this the long and proper way, or the simple and easy way.

The long way:

First, we move both logs to the same side of the equation:

log (2x)- log (24) =0

Now we can combine the logs (reminder, when you subtract logs, you divide the terms inside of them):

$log(\frac{(2x)}{24})=0$

Let's rewrite the equation in exponential form:

$\frac{2x}{24}=10^0$

Anything raised to the power equals , so we can simplify and solve from here:

$\frac{2x}{24}=1$

2x=24

x=12

The short way:

First, we cancel the log terms (because the base is the same, and all we have are the log terms):

2x=24

Then we divide by :

x=12

Report an Error

Example Question #3121 : Algebra Ii

$\log_{8}64$ = _______

Possible Answers:

Correct answer:

Explanation:

$\log_{b}a$ is equal to $b^{x}=a$ ,

so in this case it is

$8^{x}=64$ ,

and

x=2

Report an Error

Example Question #1 : Graphing Logarithmic Functions

Give the -intercept of the graph of the function

$f (x) = \ln (x + 4 ) - 7$

to two decimal places.

Possible Answers:

$\left ( 0, 20.09 \right )$

$\left (0, 1 092.63 \right )$

$\left (0, 5.75 \right )$

The graph has no -intercept.

$\left ( 0 , -5.61 \right )$

Correct answer:

$\left ( 0 , -5.61 \right )$

Explanation:

Set x = 0 and solve:

$f(x) = \ln (x + 4 ) - 7$

$f(x) = \ln ( 0 + 4 ) - 7 = \ln 4 - 7 \approx 1.39 - 7 \approx -5.61$

The -intercept is $\left ( 0 , -5.61 \right )$ .

Report an Error

Example Question #1 : Graphing Logarithmic Functions

Give the intercept of the graph of the function

$f (x) = \ln (x + 4 ) - 7$

to two decimal places.

Possible Answers:

$\left ( 20.09, 0 \right )$

$\left (1 092.63, 0 \right )$

$\left ( -5.61,0 \right )$

$\left ( 5.75,0 \right )$

The graph has no -intercept.

Correct answer:

$\left (1 092.63, 0 \right )$

Explanation:

Set f (x) = 0 and solve:

$\ln (x + 4 ) - 7 = 0$

$\ln (x + 4 ) =7$

$e ^{\ln (x + 4 ) } =e^{7}$

$x + 4 \approx 1,096.63$

$x \approx 1,092.63$

The -intercept is $\left (1,092.63, 0 \right )$ .

Report an Error

View Algebra 2 Tutors

Jonathan
Certified Tutor

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

View Algebra 2 Tutors

Armon
Certified Tutor

Loyola University-Chicago, Bachelor of Science, Biology, General. Columbia College-Chicago, Bachelor of Science, Graphic Desi...

View Algebra 2 Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

All Algebra II Resources

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

Popular Subjects

GRE Tutors in Los Angeles, Reading Tutors in New York City, GMAT Tutors in Phoenix, English Tutors in New York City, LSAT Tutors in San Diego, Math Tutors in Seattle, Computer Science Tutors in San Francisco-Bay Area, English Tutors in Boston, Statistics Tutors in San Francisco-Bay Area, MCAT Tutors in Washington DC

Popular Courses & Classes

ISEE Courses & Classes in Miami, SSAT Courses & Classes in Miami, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Atlanta, GRE Courses & Classes in Los Angeles, MCAT Courses & Classes in Houston, GMAT Courses & Classes in San Diego, GRE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Seattle

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Miami, LSAT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Philadelphia, SAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in San Diego, MCAT Test Prep in Chicago, ISEE 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

Algebra II : Solving and Graphing Logarithms

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #71 : Solving And Graphing Logarithms

Example Question #72 : Solving Logarithms

Example Question #211 : Logarithms

Example Question #74 : Solving Logarithms

Example Question #75 : Solving Logarithms

Example Question #76 : Solving Logarithms

Example Question #211 : Logarithms

Example Question #3121 : Algebra Ii

Example Question #1 : Graphing Logarithmic Functions

Example Question #1 : Graphing Logarithmic Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: