Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Exponential and Logarithmic Functions

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Exponential And Logarithmic Functions

You are given that $\log_{10} x = A$ and $\log_{10} y = B$ .

Which of the following is equal to $100^{2A-B}$ ?

Possible Answers:

$\frac{x}{\sqrt{y}}$

$\frac{x^{4}}{y^{2}}$

$\frac{y^{2}}{x^{4}}$

$x^{4}y^{2}$

$\frac{2x}{y}$

Correct answer:

$\frac{x^{4}}{y^{2}}$

Explanation:

Since $\log_{10} x = A$ and $\log_{10} y = B$ , it follows that $10^{A} = x$ and $10^{B} = y$

$100^{2A-B} = \left( 10^{2} \right ) ^{2A-B} =10^{2 (2A-B)} =10^{4A-2B}=\frac{10^{4A}}{10^{2B}} =\frac{\left ( 10^{A}\right )^4}{\left (10^{B}\right )^2}=\frac{x^4}{y^2}$

Report an Error

Example Question #1 : Solving Logarithms

$\textup{Solve for }x\textup{: }\,\log_{2}32=x$

Possible Answers:

Correct answer:

Explanation:

$\textup{This can be re-written as an exponent problem: } 2^{x}=32$

$2\times2\times2\times2\times2=32\:\textup{ so }32=2^{5}\:\:\:x=5$

Report an Error

Example Question #2 : Solving Logarithms

What is $log_{2}(8)$ ?

Possible Answers:

$\frac{1}{8}$

Correct answer:

Explanation:

Recall that by definition a logarithm is the inverse of the exponential function. Thus, our logarithm corresponds to the value of in the equation:

$2^{x} = 8$ .

We know that $2^{3} = 8$ and thus our answer is .

Report an Error

Example Question #1 : Properties Of Logarithms

Solve for : $\log_{2}\left ( x+4 \right ) + \log_{2}\left ( x+5 \right ) = \log_{2} 6$

Possible Answers:

$x = 2 \textrm{ or }x = 7$

$x = 1 \textrm{ or }x = \log_{2}7$

$x = -7 \textrm{ or }x = -2$

$x = 4 \textrm{ or }x = 128$

The correct solution set is not included among the other choices.

Correct answer:

The correct solution set is not included among the other choices.

Explanation:

$\log_{2}\left ( x+4 \right ) + \log_{2}\left ( x+5 \right ) = \log_{2} 6$

$\log_{2} \left[ \left ( x+4 \right )\left ( x+5 \right ) \right ] = \log_{2} 6$

$2^{ \log_{2} \left[ \left ( x+4 \right )\left ( x+5 \right ) \right ] }=2^{ \log_{2} 6}$

(x + 4)(x + 5) = 6

FOIL: $x^{2} + 4x + 5x + 4 \cdot 5 = 6$

$x^{2} + 9x + 20 = 6$

$x^{2} + 9x + 20 - 6 = 6- 6$

$x^{2} + 9x + 14 = 0$

(x + 2) (x + 7) = 0

$x + 2 = 0 \textrm{ or }x + 7 = 0$

$x = -2 \textrm{ or } x = -7$

These are our possible solutions. However, we need to test them.

$\log_{2}\left ( x+4 \right ) + \log_{2}\left ( x+5 \right ) = \log_{2} 6$

$\log_{2}\left ( -2+4 \right ) + \log_{2}\left ( -2+5 \right ) = \log_{2} 6$

$\log_{2}2 + \log_{2}3 = \log_{2} 6$

$\log_{2}2 = 1$

$\log_{2}3 = \frac{\ln 3}{\ln 2} \approx \frac{1.10}{0.69} \approx 1.59$

$\log_{2}6 = \frac{\ln 6}{\ln 2} \approx \frac{1.79}{0.69} \approx 2.59$

The equation becomes 1 + 1.59 = 2.59 . This is true, so x = -2 is a solution.

x = -7 :

$\log_{2}\left ( x+4 \right ) + \log_{2}\left ( x+5 \right ) = \log_{2} 6$

$\log_{2}\left ( -7+4 \right ) + \log_{2}\left ( -7+5 \right ) = \log_{2} 6$

$\log_{2}\left (-3 \right ) + \log_{2}\left (-2 \right ) = \log_{2} 6$

However, negative numbers do not have logarithms, so this equation is meaningless. x = -7 is not a solution, and x = -2 is the one and only solution. Since this is not one of our choices, the correct response is "The correct solution set is not included among the other choices."

Report an Error

Example Question #1 : Simplifying Exponential Functions

$\textup{Which of the following expressions is equivalent to }\sqrt{\frac{x^{4}y^{11}z^{5}}{x^{2}y^{5}z^{7}}} \textup{ ?}$

Possible Answers:

$\frac{xy^{3}}{z}$

$\frac{xy^{3}}{z^{2}}$

$\frac{x^{2}y^{3}}{x^{2}}$

$\textup{None of the other answers}$

$\frac{xy^{4}}{z}$

Correct answer:

$\frac{xy^{3}}{z}$

Explanation:

$\textup{Reduce the fraction by subtracting exponents, then halve all exponents to find the square root.}$

$\sqrt{\frac{x^{4}y^{11}z^{5}}{x^{2}y^{5}z^{7}}} =\sqrt{\frac{x^{2}y^{6}}{z^{2}}}\:\:=\frac{xy^{3}}{z}$

Report an Error

View Tutors

Anjali
Certified Tutor

Delhi University, Bachelor of Science, Physics. Kumuan University, Master of Science, Physics.

View Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

View Tutors

Bhavana
Certified Tutor

Indian Institute of Science Education and Research, Tirupati, Master's/Graduate, Physics and biology .

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in San Francisco-Bay Area, Spanish Tutors in New York City, Biology Tutors in San Francisco-Bay Area, LSAT Tutors in Seattle, English Tutors in Denver, English Tutors in Phoenix, GMAT Tutors in Dallas Fort Worth, Statistics Tutors in Philadelphia, English Tutors in Seattle, MCAT Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Seattle, MCAT Courses & Classes in Denver, SAT Courses & Classes in Phoenix, GRE Courses & Classes in Denver, SSAT Courses & Classes in Atlanta, SAT Courses & Classes in Denver, GMAT Courses & Classes in Chicago, MCAT Courses & Classes in San Diego, ISEE Courses & Classes in Los Angeles

Popular Test Prep

ACT Test Prep in Atlanta, SAT Test Prep in Denver, ISEE Test Prep in Chicago, LSAT Test Prep in New York City, GMAT Test Prep in Chicago, SSAT Test Prep in Washington DC, SAT Test Prep in New York City, MCAT Test Prep in Houston, ACT Test Prep in Boston, GRE Test Prep in Dallas Fort Worth

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

High School Math : Exponential and Logarithmic Functions

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Exponential And Logarithmic Functions

Example Question #1 : Solving Logarithms

Example Question #2 : Solving Logarithms

Example Question #1 : Properties Of Logarithms

Example Question #1 : Simplifying Exponential Functions

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: