Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Log-Base-10

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 #41 : Logarithms

Solve: 2log(300)

Possible Answers:

4log(2)+2

2log(3)+2

3log(2)+2

2log(3)+4

3log(2)+4

Correct answer:

2log(3)+4

Explanation:

Break up log(300) using log rules. The log has a default base of ten.

$log(A\times B) = log(A)+log(B)$

$log(300) = log(3)+log(100)=log_{10}(3)+log_{10}(10^2)$

The exponent can be brought down as the coefficient since the bases of the second term are common.

$log_{10}(3)+log_{10}(10^2) =log_{10}(3)+2log_{10}(10) = log(3)+2$

This means that: 2log(300)=2[ log(3)+2] = 2log(3)+4

The answer is: 2log(3)+4

Report an Error

Example Question #22 : Log Base 10

Evaluate: $2log_{10}(\frac{1}{1000})$

Possible Answers:

$\frac{2}{3}$

$\frac{1}{5}$

$\frac{1}{50}$

Correct answer:

Explanation:

We will need to write fraction in terms of the given base of log, which is ten.

$2log_{10}(\frac{1}{1000})=2log_{10}(10^{-3})$

According to the log rules:

$log_{x}(x^Y) =Y$

This means that the expression of log based 10 and the power can be simplified.

$2log_{10}(10^{-3}) =2\cdot -3 = -6$

The answer is:

Report an Error

Example Question #281 : Mathematical Relationships And Basic Graphs

Evaluate $\log_{8}172$ to the nearest tenth.

Possible Answers:

2.1

2.9

2.3

2.5

2.7

Correct answer:

2.5

Explanation:

Since most calculators only have common and natural logarithm keys, this can best be solved as follows:

By the Change of Base Property of Logarithms, if M,N,a > 0 and $a, M \ne 1$ ,

$\log_{M}N = \frac{\log_{a}N}{\log_{a}M}$

Setting M = 8, N = 172, a = 10 , we can restate this logarithm as the quotient of two common logarithms, and calculate accordingly:

$\log_{8}172 = \frac{\log 172}{\log 8}\approx \frac{2.2355 }{0.9031}\approx 2.4754$

or, when rounded, 2.5.

This can also be done with natural logarithms, yielding the same result.

$\log_{8}172 = \frac{\ln 172}{\ln 8} \approx \frac{5.1475}{2.0794}\approx 2.4754$

Rond to one decimal place.

2.5

Report an Error

Example Question #41 : Understanding Logarithms

Solve for in the equation:

-log(x)=4.2

Possible Answers:

$x=e^{-4.2}$

$x=10^{-4.2}$

$x=10^{-log(4.2)}$

$x=e^{4.2}$

Correct answer:

$x=10^{-4.2}$

Explanation:

This question tests your understanding of log functions.

log(x)=y can be converted to the form $x=10^{y}$ .

In this problem, make sure to divide both sides by in order to put it in the above form, where log(x)=-4.2 . Remember $log(x)=log_{10}(x)$ .

Therefore,

$log_{10}(x)=-4.2 \rightarrow x=10^{-4.2}$

Report an Error

Example Question #281 : Mathematical Relationships And Basic Graphs

Evaluate .

$5 ^{x} = 12$

Possible Answers:

$x= \log 7$

$x=\frac{\log 12}{\log 5}$

$x= \frac{ \log 5}{12}$

$x= \frac{ \log 12 }{5}$

$x=\frac{ \log 5}{\log 12}$

Correct answer:

$x=\frac{\log 12}{\log 5}$

Explanation:

Take the common logarithm of both sides, and take advantage of the property of the logarithm of a power:

$5 ^{x} = 12$

$\log 5 ^{x} = \log 12$

$x \log 5 = \log 12$

$\frac{x \log 5 }{\log 5 }=\frac{ \log 12}{\log 5}$

$x=\frac{ \log 12}{\log 5}$

Report an Error

View Algebra 2 Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Algebra 2 Tutors

Marie
Certified Tutor

Silliman University, Master of Science, Mathematics.

View Algebra 2 Tutors

Gautam
Certified Tutor

Oregon State University, Bachelor of Science, Biochemistry and Molecular Biology. Oregon State University, Bachelor of Scienc...

All Algebra II Resources

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

Popular Subjects

Computer Science Tutors in Denver, French Tutors in Miami, Algebra Tutors in Denver, GRE Tutors in Denver, Statistics Tutors in Philadelphia, French Tutors in Chicago, SSAT Tutors in Atlanta, MCAT Tutors in San Francisco-Bay Area, Biology Tutors in Atlanta, LSAT Tutors in Washington DC

Popular Courses & Classes

GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in San Diego, Spanish Courses & Classes in Houston, Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Chicago, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Houston, Spanish Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Philadelphia, SSAT Test Prep in Miami, GMAT Test Prep in Seattle, ISEE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Denver, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Seattle, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Boston

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 : Log-Base-10

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Logarithms

Example Question #22 : Log Base 10

Example Question #281 : Mathematical Relationships And Basic Graphs

Example Question #41 : Understanding Logarithms

Example Question #281 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: