We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Solving 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

← Previous 1 2 3 4 5 6 7 8 Next →

Example Question #164 : Logarithms

Solve the equation

$\ln(3x-2)=\ln(6x)$

Possible Answers:

$x=\frac{-2}{3}$

No Solution

x=2

x=1

$x=\frac{2}{3}$

Correct answer:

No Solution

Explanation:

Set the arguments of the natural log equal and solve for

3x-2=6x

-2=3x

$\frac{-2}{3}=x$

However, you cannot take the natural log of a negative number. Therefore; there is No Solution

Report an Error

Example Question #165 : Logarithms

Solve:

$\log_{2}24$

Possible Answers:

$\log12$

$-\frac{\log24}{\log2}$

$\log24$

$\frac{\log24}{\log2}$

Correct answer:

$\frac{\log24}{\log2}$

Explanation:

To solve this problem, it is easiest to start by thinking about what the logarithm means:

2^x=24

Now, we take the log of both sides (either base-10 or natural):

$\log(2^x)=\log24$

Next, using the properties of logarithms, we can bring the exponent x in front of the logarithm:

$x\log2=\log24$

Finally, solve for x:

$x=\frac{\log24}{\log2}$

Report an Error

Example Question #21 : Solving Logarithms

Evaluate

$\log_5 25 = x$

Possible Answers:

Correct answer:

Explanation:

Logarithms are inverses of exponents.

$\log_5 25$ is asking how many fives multiplied together are equal to 25.

The formula to solve logarithmic equations is as follows.

$log_ab=c\Rightarrow a^c=b$

Applying this formula to our particular problem results in the following.

$\log_5 25\Rightarrow 5^x=25$

5^2 = 5*5 = 25

So x= 2 .

Report an Error

Example Question #167 : Logarithms

Solve:

$\log_84+\log_810$

Possible Answers:

$\frac{\log14}{\log8}$

$\log32$

$\frac{\log40}{\log8}$

$\log5$

Correct answer:

$\frac{\log40}{\log8}$

Explanation:

To solve, we must keep in mind that a logarithm is asking the following:

$\log_ab$ means a^x=b , and we must find x.

First, we can rewrite the sum of the base-8 logarithms as a product (this is a property of logarithms):

$\log_8(4\cdot 10)=\log_840$

Now, we use the above formula to find what this numerically equals:

8^x=40

Take the natural or common logarithm of both sides, which allows us to bring the power x in front of the logarithm:

$\log8^x=\log40$

$x\log8=\log40$

$x=\frac{\log40}{\log8}$

Report an Error

Example Question #168 : Logarithms

Solve for x:

$4^x=3^{x^2}$

Possible Answers:

$\log\frac{3}{4}$

$\log\frac{4}{3}$

$\log1$

$\frac{\log4}{\log3}$

$\frac{\log3}{\log4}$

Correct answer:

$\frac{\log4}{\log3}$

Explanation:

To solve for x, we must take the logarithm of both sides (common or natural, it doesn't matter):

$\log(4^x)=\log(3^{x^2})$

In doing this, we can now bring the exponents in front of the logarithms:

$x\log4=x^2\cdot\log3$

Now, solve for x:

$\log4=x\log3$

$x=\frac{\log4}{\log3}$

Report an Error

Example Question #169 : Logarithms

If $log_{m}(2)=.387$ and $log_{m}(3)=.613$ , what is ?

Possible Answers:

Correct answer:

Explanation:

First, we know from logarithmic properties that:

$log_{n}(n)=1$

So if we can find a combination of our knowns that equal , we should be able to figure out . It may take some guess and check, but:

.387 + .613 = 1

That would equate to:

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

Using our log properties, we can simplify into:

$log_{m}(2\cdot 3)=1$

$log_{m}(6)=1$

That means that:

m=6

Report an Error

Example Question #21 : Solving Logarithms

Evaluate $log_{100}(10000)$ .

Possible Answers:

100

Correct answer:

Explanation:

There are a few ways to go about this, but let's use a change of base to make the problem easier to work without using a calculator. First, we know that:

$log_{m}(n)=\frac{log_x(m)}{log_x(n)}$

We can choose any value for that we would like here, so to make things simple, let's put this problem in base :

$log_{100}(10000) = \frac{log_{10}(10000)}{log_{10}(100)} = \frac{4}{2} = 2$

Report an Error

Example Question #21 : Solving Logarithms

Evaluate log_3(27) .

Possible Answers:

Correct answer:

Explanation:

We can take this problem and expand it a bit, which will make things easier in the long run. We know that:

$log_3(27)=log_3(3\cdot 3\cdot 3)$

Using one of our logarithmic properties, we can expand even further:

$log_3(3\cdot 3\cdot 3)=log_3(3)+log_3(3)+log_3(3)$

Another log property states that:

log_x(x)=1

So:

log_3(3)+log_3(3)+log_3(3) = 1+1+1 = 3

Report an Error

Example Question #22 : Solving Logarithms

Solve:

$\log_4 16^x=10$

Possible Answers:

x=5

x=0

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

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

x=1

Correct answer:

x=5

Explanation:

To solve for x, remember that exponents inside logarithms can be moved to the front of the logarithm:

$x\cdot \log_416=10$

Next, we can rewrite the logarithm as the number it equals, and solve for x:

$x\cdot2=10$

x=5

Report an Error

Example Question #23 : Solving Logarithms

Solve: ln(2x) = 100

Possible Answers:

$2e^{100}$

$e^{50}$

$\frac{e^{100}}{2}$

Correct answer:

$\frac{e^{100}}{2}$

Explanation:

In order to solve for the x-variable, we will need to exponential function both sides of the equation in order to eliminate the natural log.

$e^{ln(2x) }= e^{100}$

The equation becomes:

$2x= e^{100}$

Divide by two on both sides.

$\frac{2x}{2}= \frac{e^{100}}{2}$

$x= \frac{e^{100}}{2}$

The answer is: $\frac{e^{100}}{2}$

Report an Error

← Previous 1 2 3 4 5 6 7 8 Next →

View Algebra 2 Tutors

George
Certified Tutor

Colby College, Bachelors, Economics/Spanish. Massachusetts Institute of Technology, Masters, Urban Studies.

View Algebra 2 Tutors

Jitendra
Certified Tutor

BHU, Bachelor, Mathematics.

View Algebra 2 Tutors

Thushan
Certified Tutor

Guilford Technical Community College, Associate in Science, Mechanical Engineering. North Carolina State University at Raleig...

All Algebra II Resources

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

Popular Subjects

GRE Tutors in Houston, Math Tutors in Seattle, Physics Tutors in Miami, MCAT Tutors in Seattle, Reading Tutors in San Francisco-Bay Area, Algebra Tutors in Houston, Statistics Tutors in Boston, SSAT Tutors in Boston, Statistics Tutors in Dallas Fort Worth, LSAT Tutors in Houston

Popular Courses & Classes

GRE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Chicago, ISEE Courses & Classes in Houston, GMAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in San Diego, Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Boston, ISEE Courses & Classes in Denver, GRE Courses & Classes in Philadelphia

Popular Test Prep

ISEE Test Prep in Los Angeles, ACT Test Prep in San Diego, LSAT Test Prep in Miami, SSAT Test Prep in Seattle, ACT Test Prep in Los Angeles, ISEE Test Prep in Phoenix, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Seattle, ACT 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 : Solving Logarithms

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #164 : Logarithms

Example Question #165 : Logarithms

Example Question #21 : Solving Logarithms

Example Question #167 : Logarithms

Example Question #168 : Logarithms

Example Question #169 : Logarithms

Example Question #21 : Solving Logarithms

Example Question #21 : Solving Logarithms

Example Question #22 : Solving Logarithms

Example Question #23 : Solving Logarithms

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: