Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Understanding 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 #21 : Natural Log

Solve: ln(2x-e) = 3

Possible Answers:

$\frac{e^3+e}{2}$

$\frac{(e+1)^3}{2}$

$\frac{e^3-e}{2}$

$\frac{3}{2}e$

$\frac{9-e}{3}$

Correct answer:

$\frac{e^3+e}{2}$

Explanation:

In order to eliminate the natural log, which has a base of , we will need to raise both side as powers of .

$e^{ln(2x-e)} = e^3$

The equation can be simplified to:

2x-e = e^3

Add on both sides.

2x-e +e= e^3+e

2x= e^3+e

Divide by two on both sides.

$\frac{2x}{2}= \frac{e^3+e}{2}$

The answer is: $\frac{e^3+e}{2}$

Report an Error

Example Question #22 : Natural Log

Try without a calculator:

Which expression is not equivalent to 1?

Possible Answers:

$i^{4}$

$1,000^{\frac{1}{1,000}}$

$\log 10$

$1,000,000^{0}$

$\ln e$

Correct answer:

$1,000^{\frac{1}{1,000}}$

Explanation:

$1,000^{\frac{1}{1,000}}$ is the correct choice.

For all a,N for which the expressions are defined,

$a ^{\frac{1}{N}} = \sqrt[N]{a}$ .

Setting a=1,000, N = 1,000 , this equation becomes

$1,000 ^{\frac{1}{1,000}} = \sqrt[1,000]{1,000}$ - that is, the one thousandth root of 1,000. This is not equal to 1, since if it were, it would hold that $1^{1,000} = 1,000$ - which is not true.

Of the other four expressions:

$\log 10$ , the common, or base ten, logarithm of 10, can be rewritten as $\log_{10}10$ , and $\ln e$ , the natural, or base , logarithm of , can be rewritten as $\log_{e}e$ . A property of logarithms states that for all $N > 0, N \ne 1$ , $\log_{N}N = 1$ . Therefore, $\log 10 = \log_{10}10 = 1$ and $\ln e = \log_{e}e = 1$ .

$1,000,000^{0} = 1$ , since any nonzero number raised to the power of 0 is equal to 1.

By the Power of a Power Property,

$i^{4} = i ^{2 \cdot 2} =( i^{2} )^{2}$

$i^{2} = -1$ , so

$i^{4} = ( -1)^{2}= 1$

Report an Error

Example Question #1 : Logarithms

Based on the definition of logarithms, what is ${\log_{10}1000}$ ?

Possible Answers:

100

Correct answer:

Explanation:

For any equation $\log_{10}(y) = x$ , $10^{x } = y$ . Thus, we are trying to determine what power of 10 is 1000. 1000 = 10^3 , so our answer is 3.

Report an Error

Example Question #1 : Log Base 10

$7 ^{x} = 1,000$

Evaluate .

Possible Answers:

$x = 1,000 - \log 7$

$x = 3 - \log 7$

$x = \frac{3}{\log 7}$

$x = \frac{1,000}{\log 7}$

$\log 993$

Correct answer:

$x = \frac{3}{\log 7}$

Explanation:

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

$7 ^{x} = 1,000$

$7 ^{x} = 10^{3}$

$\log 7 ^{x} = \log 10^{3}$

$x \log 7 = 3 \log 10$

$x \log 7 = 3 \cdot 1$

$x \log 7 = 3$

$\frac{x \log 7}{\log 7} = \frac{3}{\log 7}$

$x = \frac{3}{\log 7}$

Report an Error

Example Question #1 : Log Base 10

What is the value of $\log{10000000}$ ?

Possible Answers:

5.68

6.97

7.31

8.13

Correct answer:

Explanation:

Base-10 logarithms are very easy if the operands are a power of . Begin by rewriting the question:

$\log{10000000}$

Becomes...

$\log{10^7}$

because 10^7=10000000

Applying logarithm rules, you can factor out the :

$7\log{10}$

Now, $\log{10}$ is .

Therefore, your answer is .

Report an Error

Example Question #1 : Log Base 10

What is the value of $\log{100000}$ ?

Round to the nearest hundreth.

Possible Answers:

5.01

5.10

4.52

Correct answer:

Explanation:

Base-10 logarithms are very easy if the operands are a power of . Begin by rewriting the question:

$\log{100000}$

Becomes...

$\log{10^5}$

because 10^5=100000

Applying logarithm rules, you can factor out the :

$5\log{10}$

Now, $\log{10}$ is .

Therefore, your answer is .

Report an Error

Example Question #1 : Log Base 10

Many textbooks use the following convention for logarithms:

$log(x) = log_{10}(x)$

ln(x) = log_e(x)

lg(x)=log_2(x)

What is the value of log1,000 ?

Possible Answers:

100

Correct answer:

Explanation:

Remember:

log_ab=c is the same as saying a^c = b .

So when we ask "What is the value of log(1,000) ?", all we're asking is "10 raised to which power equals 1,000?" Or, in an expression:

10^? = 1,000 .

From this, it should be easy to see that log(1000)=3 .

Report an Error

Example Question #1 : Log Base 10

Evaluate the following expression:

$\small \log (1000)$

Possible Answers:

$\small 10$

$\small 1$

$\small 5$

$\small 3$

$\small 2$

Correct answer:

$\small 3$

Explanation:

Without a subscript a logarithmic expression is base 10.

The expression $\small \log(1000)=\log _{10}(1000)$

The logarithmic expression is asking 10 raised to what power equals 1000 or what is x when

$\small 10^{x}=1000$

We know that $\small 10^{3}=1000$

so $\small \log (1000)=3$

Report an Error

Example Question #7 : Log Base 10

Assuming the value of is positive, simplify: $\log_{10}10^{3x+2}$

Possible Answers:

-3x-2

30x+20

-30x-20

3x+2

Correct answer:

3x+2

Explanation:

Rewrite the logarithm in division.

$\log_{10}10^{3x+2} = \frac{\log{10}^{3x+2}}{\log 10}$

As a log property, we can pull down the exponent of the power in front as the coefficient.

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

Cancel out the $\log(10)$ .

The answer is: 3x+2

Report an Error

Example Question #8 : Log Base 10

Solve the following:

$\log10000+\log10$

Possible Answers:

$\log10010$

Correct answer:

Explanation:

When the base isn't explicitly defined, the log is base 10. For our problem, the first term

$\log 10000=x$

is asking:

10^x=10000

x=4

For the second term,

$\log(10)=y$

is asking:

10^y=10

y=1

So, our final answer is 4+1=5

Report an Error

View Algebra 2 Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Algebra 2 Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Algebra 2 Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

All Algebra II Resources

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

Popular Subjects

Calculus Tutors in Miami, GMAT Tutors in San Diego, Chemistry Tutors in Seattle, Calculus Tutors in Seattle, SAT Tutors in Phoenix, ACT Tutors in Seattle, Algebra Tutors in Dallas Fort Worth, MCAT Tutors in Seattle, Reading Tutors in Seattle, French Tutors in Phoenix

Popular Courses & Classes

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

Popular Test Prep

GRE Test Prep in Washington DC, GMAT Test Prep in Miami, ACT Test Prep in San Diego, SSAT Test Prep in San Diego, GMAT Test Prep in Seattle, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle, GMAT Test Prep in Washington DC, ISEE Test Prep in San Francisco-Bay Area, GRE 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 : Understanding Logarithms

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Natural Log

Example Question #22 : Natural Log

Example Question #1 : Logarithms

Example Question #1 : Log Base 10

Example Question #1 : Log Base 10

Example Question #1 : Log Base 10

Example Question #1 : Log Base 10

Example Question #1 : Log Base 10

Example Question #7 : Log Base 10

Example Question #8 : Log Base 10

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: