We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Solving Logarithmic Functions

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 Next →

Example Question #61 : Exponential And Logarithmic Functions

Solve for x:

$log_{3}x=3$

Possible Answers:

x=54

x=36

x=9

x=27

Correct answer:

x=27

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{3}x=3$

$3^{3}=x$

x=27

Report an Error

Example Question #71 : Exponential And Logarithmic Functions

Solve for x:

$log_{2}x=4$

Possible Answers:

x=16

x=2

x=32

x=8

Correct answer:

x=16

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{2}x=4$

$2^{4}=x$

x=16

Report an Error

Example Question #72 : Exponential And Logarithmic Functions

Solve for x:

$log_{4}x=2$

Possible Answers:

x=8

x=64

x=16

x=2

Correct answer:

x=16

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{4}x=2$

$4^{2}=x$

x=16

Report an Error

Example Question #73 : Exponential And Logarithmic Functions

Solve for x:

$log_{7}x=3$

Possible Answers:

x=343

x=21

x=2187

x=49

Correct answer:

x=343

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{7}x=3$

$7^{3}=x$

x=343

Report an Error

Example Question #71 : Exponential And Logarithmic Functions

What is the correct value of ? 3log_b (10)=1

Possible Answers:

log(300)

1000

300

$\frac{1}{1000}$

Correct answer:

1000

Explanation:

Divide by three on both sides.

$\frac{3log_b (10)}{3}=\frac{1}{3}$

$log_b (10)=\frac{1}{3}$

If we would recall 10^2 = 100 and $log_{10}(100) = 2$ , this indicates that:

$b^{\frac{1}{3}} = 10$

Cube both sides to isolate b.

$(b^{\frac{1}{3}}) ^3= 10^3$

The answer is: 1000

Report an Error

Example Question #74 : Exponential And Logarithmic Functions

What is the value of 3log_4(64) ?

Possible Answers:

Correct answer:

Explanation:

The expression can be rewritten as:

$3log_4(64) = 3(\frac{log(64)}{log (4)}) = 3(\frac{log(4^3)}{log(4^1)}) =3(\frac{3log(4)}{log(4)})$

The answer is:

Report an Error

Example Question #75 : Exponential And Logarithmic Functions

Solve this logarithm: $\log_{10} (5x-1)=\log_{10} (x+9)$

Possible Answers:

$x=\frac{1}{5}$

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

None of these

$x=\frac{10}{2}$

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

Correct answer:

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

Explanation:

By the one-to-one property of logarithms we are able to set 5x-1=x+9 and solve.

$5x-1=x+9\rightarrow 5x=x+10\rightarrow 4x=10\rightarrow \boldsymbol{x=\frac{5}{2}}$

Report an Error

Example Question #21 : Solving Logarithmic Functions

Solve the logarithm: $-8-3\ln x=13$

Possible Answers:

$x\approx 3.12 \times 10^{4}$

$x\approx 3.12 \times 10^{-4}$

$x\approx 9.12 \times 10^{-4}$

$x\approx 2.19\times 10^{-4}$

$x\approx 1.92 \times 10^{-4}$

Correct answer:

$x\approx 9.12 \times 10^{-4}$

Explanation:

$-8-3\ln x=13$

add 8 to both sides:

$-3\ln x=21$

divide both sides by -3:

$\ln x=-7$

exponentiate both sides:

$e^{\ln x}=e^{-7}$

$x=\boldsymbol{e^{-7}\approx9.12\times 10^{-4}}$

Report an Error

← Previous 1 2 3 Next →

View College Algebra Tutors

Kayley
Certified Tutor

New Mexico State University-Main Campus, Bachelor of Science, Biology, General.

View College Algebra Tutors

Akunna
Certified Tutor

Bergen Community College, Associate in Science, Natural Sciences. Long Island University-Brooklyn Campus, Current Grad Studen...

View College Algebra Tutors

Harold
Certified Tutor

University of Waterloo, Bachelors, Physics. University of North Carolina at Chapel Hill, Masters, MBA.

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Washington DC, Physics Tutors in Chicago, LSAT Tutors in Philadelphia, French Tutors in Atlanta, ACT Tutors in Philadelphia, SAT Tutors in Chicago, Algebra Tutors in Atlanta, English Tutors in Chicago, Algebra Tutors in San Francisco-Bay Area, GRE Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in Miami, SAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, MCAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Atlanta, ACT Courses & Classes in Houston, MCAT Courses & Classes in Phoenix, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Los Angeles

Popular Test Prep

ACT Test Prep in Chicago, MCAT Test Prep in Atlanta, MCAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Atlanta, SAT Test Prep in Phoenix, GRE Test Prep in Philadelphia, GRE Test Prep in San Diego, MCAT Test Prep in Philadelphia, ISEE Test Prep in New York City, MCAT Test Prep in Phoenix

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

College Algebra : Solving Logarithmic Functions

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #61 : Exponential And Logarithmic Functions

Example Question #71 : Exponential And Logarithmic Functions

Example Question #72 : Exponential And Logarithmic Functions

Example Question #73 : Exponential And Logarithmic Functions

Example Question #71 : Exponential And Logarithmic Functions

Example Question #74 : Exponential And Logarithmic Functions

Example Question #75 : Exponential And Logarithmic Functions

Example Question #21 : Solving Logarithmic Functions

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: