We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Logarithms

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Evaluating Logarithms

Solve: log_4 256=x

Possible Answers:

x=10

x=-4

x=4

x=6

Correct answer:

x=4

Explanation:

Step 1: Re-write the log equation as an exponential equation. To do this, take the base of the log function and raise it to the number on the right side of the equal sign. This new exponent is equal to the number to the right of the log base.

4^x=256

Step 2: Re-write the right hand side as a power of 4..

256=4^4

Step 3: Re-write the equation

4^x=4^4

Step 4: We have the same base, so we can equal the exponents..

x=4

Report an Error

Example Question #1 : Evaluating Logarithms

$Solve\ for\ x: log_{x}(49)=2$

Possible Answers:

49^2

$\pm7$

24.5

Correct answer:

$\pm7$

Explanation:

In order to solve for x, we must first rewrite the log in exponential form.

Every log is written in the below general form:

$log_{base}(result)=exponent\ is\ rewritten\ as: base^e^x^p^o^n^e^n^t=result$

In this case we have:

$log_{x}(49)=2$

This becomes:

x^2=49

We can solve this by taking the square root of both sides:

$\sqrt{x^2}=\sqrt{49}$

$x=\pm7$

Report an Error

Example Question #1 : Logarithms

Solve for :

log_4 4096=x

Possible Answers:

x=7

x=9

x=4

x=2

x=6

Correct answer:

x=6

Explanation:

Use rules of logarithms...

Take the base of the log and raise it to the number on the right side of the equal sign (which becomes the exponent):

4^x=4096

$\\4^x=16^3 \\4^x=(4^2)^3 \\4^x=4^6 \\x=6$

Report an Error

Example Question #1 : Evaluating Logarithms

Evaluate: $\log_6 46656=x$

Possible Answers:

Correct answer:

Explanation:

Step 1: Write the expression in exponential form...

Given: $\log_a b=x\implies a^x=b$

$\log_6 46656=x\implies 6^x=46656$

Step 2: Convert the right hand side into a power of 6..

46656=6^6

Step 3: Re-write the equations...

6^x=6^6

Since the bases are equal, taking log of both sides will cancel them.

$\log_6 6^x=\log_6 6^6$

$\implies x=6$

Report an Error

Example Question #1 : Logarithms

$Solve\ for\ x:\ log_{2}(8)=x$

Possible Answers:

Correct answer:

Explanation:

$In\ order\ to\ solve\ for\ x\ we\ must\ know\ how\ to\ rewrite\ a\ log\ in\ exponent\ form:$

$We\ can\ use\ the\ general\ rule:\ log_{b}(a)=x\\ when\ rewritten\ in\ exponential\ form\ we\ get: b^{x}=a$

$To\ Solve\ for\ x:\ log_{2}(8)=x;\ we\ rewrite\ as\ 2^{x}=8$

$We\ know\ that\ 2^{3}=8;\ so\ the\ value\ of\ x=3$

Report an Error

Example Question #1 : Logarithmic Properties

Rewrite the following expression as a single logarithm

$5log_35x+log_3\frac{1}{4x^3}-log_3x^2$

Possible Answers:

6.06

log_33125x

$log_3\frac{3125x^3}{9}$

3.076

$log_3\frac{3125x^3}{4}$

Correct answer:

6.06

Explanation:

Recall a few properties of logarithms:

1.When adding logarithms of like base, we multiply the inside.

2.When subtracting logarithms of like base, we divide the inside.

3. When multiplying a logarithm by a number, we can raise the inside to that power.

So we begin with this:

$5log_35x+log_3\frac{1}{4x^3}-log_3x^2$

I would start with 3 to simplify the first log.

$log_3(5x)^5+log_3\frac{1}{4x^3}-log_3x^2$

$log_33125x^5+log_3\frac{1}{4x^3}-log_3x^2$

Next, use rule 1 on the first two logs.

$log_3\left(3125x^5\cdot\frac{1}{4x^3}\right)-log_3x^2$

$log_3\left(\frac{3125x^2}{4}\right)-log_3x^2$

Then, use rule 2 to combine these two.

$log_3\left(\frac{3125x^2}{4x^2}\right)=log_3\left(\frac{3125}{4}\right)\approx 6.06$

So our answer is 6.06.

Report an Error

Example Question #1 : Logarithms

$Rewrite\ as\ one\ log: [log(x)+log(z)]-log(y)$

Possible Answers:

$log\left (\frac{xy}{z} \right )$

$log\left (\frac{xz}{y} \right )$

$log\left (\frac{x+z}{y} \right )$

$log\left ({xz}-{y} \right )$

Correct answer:

$log\left (\frac{xz}{y} \right )$

Explanation:

When combining logarithms into one log, we must remember that addition and multiplication are linked and subtraction and division are linked.

log(ab)=log(a)+log(b)

$log\left (\frac{a}{b} \right )=log(a)+log(b)$

In this case we have multiplication and division - so we assume anything that is negative, must be placed in the bottom of the fraction.

[log(x)+log(z)]-log(y)=log(xz)-log(y)

$log(xz)-log(y)=log\left ( \frac{xz}{y} \right )$

Report an Error

Example Question #1 : Logarithmic Properties

$Rewrite\ in\ log\ form: 12^(^x^+^2^)=y$

Possible Answers:

$log_{12}(x+2)=y$

$log_{12}(y)=x+2$

$log_{y}(12)=x+2$

$log_{x+2}(y)=12$

Correct answer:

$log_{12}(y)=x+2$

Explanation:

When rewriting an exponential function as a log, we must follow the model below:

$log_{base}(result)=exponent$

A log is used to find an exponent. The above corresponds to the exponential form below:

base^(^e^x^p^o^n^e^n^t^)=result

$12^(^x^+^2^)=y\ rewritten\ in\ log\ form\ becomes:$

$log_{12}(y)=x+2$

$The\ base\ is\ 12,\ the\ exponent\ is\ (x+2)\ and\ the\ result\ is\ y.$

Report an Error

Example Question #1 : Logarithms

$Rewrite\ in\ exponential\ form: log_{3}(22)=y$

Possible Answers:

22^y=3

3^2^2=y

y^3=22

3^y=22

Correct answer:

3^y=22

Explanation:

In order to rewrite a log, we must remember the pattern that they follow below:

$log_{base}(result)=exponent$

In this question we have:

$log_{3}(22)=y$

$The\ base\ is\ 3,\ the\ exponent\ is\ y\ and\ the\ result\ is\ 22.$

$We\ now\ rewrite\ this\ as:\ 3^y=22$

Report an Error

Example Question #1 : Logarithms

Express $4\log_4 (x^2)-\log_4(y^{3})+\frac {1}{5}\log_4(z)$ as a single logarithm.

Possible Answers:

$\log_4 \bigg(\frac {x^8\sqrt[5]{z}}{y^{-3}}\bigg)$

$\log_4 \bigg(\frac {x^8\sqrt[3]{z}}{y^5}\bigg)$

$\log_4 \bigg(\frac {x^5\sqrt[8]{z}}{y^3}\bigg)$

$\log_4 \bigg(\frac {x^8\sqrt[5]{z}}{y^3}\bigg)$

Correct answer:

$\log_4 \bigg(\frac {x^8\sqrt[5]{z}}{y^3}\bigg)$

Explanation:

Step 1: Recall all logarithm rules:

$\log_a b+\log_a c=\log_a (bc)$

$\log_a b-\log_a c=log_a \bigg(\frac{b}{c}\bigg)$

$c\log_a b=\log_a (b^c)$

$\large a^{\frac {1}{b}}=\sqrt[b]{a}$

Step 2: Rewrite the first term in the expression..

$4\log_4 x^2=\log_4 (x^2)^4=log_4 (x^8)$

Step 3: Re-write the third term in the expression..

$\frac {1}{5}\log_4 (z)=\log_4 (z)^{\frac {1}{5}}=log_4 (\sqrt[5] {z})$

Step 4: Add up the positive terms...

$\log_4(x^8)+\log_4 (\sqrt[5]{z})=\log_4 (x^8\sqrt[5]{z})$

Step 5: Subtract the answer the other term from the answer in Step 4.

$\log_4 (x^8\sqrt[5]{z})-\log_4(y^3)=\log_4 \bigg(\frac {x^8\sqrt[5]{z}}{y^3}\bigg)$

Report an Error

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Max
Certified Tutor

SHAHiDBEHESHTiUNiVERSiTY, Bachelor of Science, Mathematics. SHAHiDBEHESHTiUNiVERSiTY, Master of Science, Mathematics.

View Tutors

Sonu
Certified Tutor

Rajasthan Technical University Kota, Bachelor, Electrical.

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Miami, Calculus Tutors in Phoenix, Math Tutors in Phoenix, ISEE Tutors in Houston, Physics Tutors in Washington DC, LSAT Tutors in Boston, English Tutors in Phoenix, LSAT Tutors in Denver, Statistics Tutors in Los Angeles, MCAT Tutors in Atlanta

Popular Courses & Classes

SAT Courses & Classes in Miami, GRE Courses & Classes in Phoenix, MCAT Courses & Classes in Denver, GRE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Denver, SSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Miami, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Denver, ACT Courses & Classes in Miami

Popular Test Prep

SAT Test Prep in Chicago, GRE Test Prep in Denver, ACT Test Prep in Boston, ACT Test Prep in Houston, GRE Test Prep in Atlanta, LSAT Test Prep in Houston, SAT Test Prep in Miami, GMAT Test Prep in Los Angeles, GRE Test Prep in Phoenix, ISEE Test Prep in Los Angeles

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

GRE Subject Test: Math : Logarithms

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Evaluating Logarithms

Example Question #1 : Evaluating Logarithms

Example Question #1 : Logarithms

Example Question #1 : Evaluating Logarithms

Example Question #1 : Logarithms

Example Question #1 : Logarithmic Properties

Example Question #1 : Logarithms

Example Question #1 : Logarithmic Properties

Example Question #1 : Logarithms

Example Question #1 : Logarithms

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: