We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Logarithms

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Logarithms

Let log 5 = 0.69897 and log 2 = 0.30103. Solve log 50

Possible Answers:

1.69897

1.39794

1.68794

1.30103

1.36903

Correct answer:

1.69897

Explanation:

Using properties of logs:

log (xy) = log x + log y

log (xⁿ) = n log x

log 10 = 1

So log 50 = log (10 * 5) = log 10 + log 5 = 1 + 0.69897 = 1.69897

Report an Error

Example Question #2 : Logarithms

y = 2^x

If y = 3, approximately what is x?

Round to 4 decimal places.

Possible Answers:

0.6309

1.5850

2.0000

1.8580

1.3454

Correct answer:

1.5850

Explanation:

To solve, we use logarithms. We log both sides and get: log3 = log2^x

which can be rewritten as log3 = xlog2

Then we solve for x: x = log 3/log 2 = 1.5850 . . .

Report an Error

Example Question #3 : Logarithms

Evaluate

log₃27

Possible Answers:

Correct answer:

Explanation:

You can change the form to

3^x= 27

x = 3

Report an Error

Example Question #1 : Logarithms

If $\small \log_{x}49=2$ , what is $\small x$ ?

Possible Answers:

$7$

$24.5$

$10$

$0$

$2401$

Correct answer:

$7$

Explanation:

If $\small \log_{x}y=z$ , then $\small x^{z}=y$

$\small x^{2}=49$

$\small x=7$

Report an Error

Example Question #1 : Logarithms

If log₄ x = 2, what is the square root of x?

Possible Answers:

Correct answer:

Explanation:

Given log₄x = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.

Report an Error

Example Question #2 : Logarithms

Solve for x in the following equation:

log₂24 - log₂3 = log_x27

Possible Answers:

–2

Correct answer:

Explanation:

Since the two logarithmic expressions on the left side of the equation have the same base, you can use the quotient rule to re-express them as the following:

log₂24 – log₂3 = log₂(24/3) = log₂8 = 3

Therefore we have the following equivalent expressions, from which it can be deduced that x = 3.

log_x27 = 3

x³ = 27

Report an Error

Example Question #2 : Logarithms

What value of satisfies the equation $\log _{x}64=2$ ?

Possible Answers:

Correct answer:

Explanation:

The answer is .

$\log _{x}64=2$ can by rewritten as $x^{2}=64$ .

In this form the question becomes a simple exponent problem. The answer is because $8^{2}=64$ .

Report an Error

Example Question #2 : Logarithms

If $\log _{2}64=x$ , what is ?

Possible Answers:

Correct answer:

Explanation:

Use the following equation to easily manipulate all similar logs:

$\log _{a}b=x$ changes to $a^{x}=b$ .

Therefore, $\log _{2}64=x$ changes to $2^{x}=64$ .

2 raised to the power of 6 yields 64, so must equal 6. If finding the 6 was difficult from the formula, simply keep multiplying 2 by itself until you reach 64.

Report an Error

Example Question #3 : Logarithms

Which of the following is a value of $x$ that satisfies $\log_{x}64=2$ ?

Possible Answers:

$4$

$32$

$8$

$16$

$2$

Correct answer:

$8$

Explanation:

The general equation of a logarithm is $\log_{x}a=b$ , and $x^{b}=a$

In this case, $x^{2}=64$ , and thus $x=8$ (or $-8$ , but $-8$ is not an answer choice)

Report an Error

Example Question #3 : Logarithms

How can we simplify this expression below into a single logarithm?

$3log(x)+\frac{1}{2}log(4y)-log(z)$

Possible Answers:

$log(2x^{3}+y^{\frac{1}{2}}-z)$

$log(\frac{2x^{3}y^{\frac{1}{2}}}{z})$

$log(\frac{4x^{3}y^{\frac{1}{2}}}{z})$

Cannot be simplified into a single logarithm

$\frac{3}{2}log(\frac{4xy}{z})$

Correct answer:

$log(\frac{2x^{3}y^{\frac{1}{2}}}{z})$

Explanation:

Using the property that $log(x^{n})=nlog(x)$ , we can simplify the expression to $log(x^{3})+log((4y)^{\frac{1}{2}})-log(z)$ .

Given that log(xy)=log(x)+log(y) and $log(\frac{x}{y})=log(x)-log(y)$

We can further simplify this equation to $log(\frac{2x^{3}y^{\frac{1}{2}}}{z})$

Report an Error

View ACT Math Tutors

Chandni
Certified Tutor

Rutgers University-New Brunswick, Current Undergrad, Cell Biology and Neuroscience.

View ACT Math Tutors

Megan
Certified Tutor

University of Wisconsin-Madison, Bachelor of Science, Chemical Engineering.

View ACT Math Tutors

Wasifuddin
Certified Tutor

University of Houston-Clear Lake, Bachelor of Science, Biology, General.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

MCAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Phoenix, LSAT Courses & Classes in New York City, SSAT Courses & Classes in New York City, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, LSAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Miami, ACT Test Prep in Denver, SSAT Test Prep in Denver, SAT Test Prep in Denver, SAT Test Prep in Boston, ISEE Test Prep in Philadelphia, ISEE Test Prep in Seattle, SSAT Test Prep in Miami, ISEE Test Prep in Los Angeles, GRE Test Prep in San Francisco-Bay Area

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

ACT Math : Logarithms

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Logarithms

Example Question #2 : Logarithms

Example Question #3 : Logarithms

Example Question #1 : Logarithms

Example Question #1 : Logarithms

Example Question #2 : Logarithms

Example Question #2 : Logarithms

Example Question #2 : Logarithms

Example Question #3 : Logarithms

Example Question #3 : Logarithms

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: