GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 19:17 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If 8^(1/2) = 4^x, what is the value of x?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58340
If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 78% (00:53) correct 22% (01:15) wrong based on 77 sessions

HideShow timer Statistics

If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/4

B. 2/3

C. 3/4

D. 4/3

E. 1

_________________

Originally posted by Bunuel on 22 Jun 2017, 05:34.
Last edited by Bunuel on 22 Jun 2017, 07:49, edited 1 time in total.
Edited the options.
Director  V
Joined: 04 Dec 2015
Posts: 745
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

1
$$8^{(\frac{1}{2})} = 4^x$$

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

$$2x = \frac{3}{2}$$

$$x = \frac{3}{4}$$ . Answer (C)...

Originally posted by sashiim20 on 22 Jun 2017, 05:44.
Last edited by sashiim20 on 22 Jun 2017, 08:04, edited 1 time in total.
Current Student P
Joined: 18 Aug 2016
Posts: 610
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

$$8^(1/2)$$ = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong
_________________
We must try to achieve the best within us

Thanks
Luckisnoexcuse
Intern  B
Joined: 29 Mar 2016
Posts: 5
Location: United States
Schools: Stern '20
GMAT 1: 720 Q48 V41 GPA: 3
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

1
8^(1/2)=4^x
2^(3/2) =2^(2x)
3/2 = 2x
x= 3/4

Bunuel, did I make a mistake or are the answers incorrect?
Current Student P
Joined: 18 Aug 2016
Posts: 610
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

1
mynamegoeson wrote:
Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

$$8^(1/2)$$ = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong

Let me correct myself

$$8^{(\frac{1}{2})} = 4^x$$
We can write it as
64^(1/4) = 64^(x/3)

x/3 = 1/4
x=3/4
_________________
We must try to achieve the best within us

Thanks
Luckisnoexcuse

Originally posted by Luckisnoexcuse on 22 Jun 2017, 06:35.
Last edited by Luckisnoexcuse on 22 Jun 2017, 06:53, edited 1 time in total.
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

1
Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

Bunuel why so many questions posted today has wrong options.. This question also has none of the options matching with the correct answer..

Please check the options again.
As for the solution .. $$8^{(\frac{1}{2})} = 4^x$$
-> 2^(3/2) = 2 ^(2x)
-> 3/2 = 2x
-> x = 3/4

No options is matching the answer...
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

1
sashiim20 wrote:
Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

$$8^{(\frac{1}{2})} = 4^x$$

$$\sqrt{2^3} = (2*2)^x$$

$$2\sqrt{2} = (2*2)^x$$

Cancelling 2 from both sides we get;

$$\sqrt{2} = (2)^x$$

$$2^{(\frac{1}{2})} = 2^x$$

$$x = \frac{1}{2}$$ . Answer (A) ...

How did you cancelled 2 from both sides ??. We can't cancel 2 like this
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4003
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

1
Top Contributor
Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

Given: $$8^{(\frac{1}{2})} = 4^x$$

Rewrite 8 as 2³ and 4 as 2² to get: (2³)^(1/2) = (2²)^x
Apply power of a power law to both sides: 2^(3/2) = 2^(2x)
So, we can conclude that 3/2 = 2x
Divide both sides by 2 to get: 3/4 = x

RELATED VIDEOS

_________________
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

mynamegoeson wrote:
Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

$$8^(1/2)$$ = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong

I don't think we can work with closest value.. No approximation is asked in question.
Also approximating 2.83 to 2 is not the right way of solving quantitative questions.. We must keep in mind that approximation should look like approximation.. I think here the options are wrong...
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

mynamegoeson wrote:
mynamegoeson wrote:
Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/2

B. 1

C. 2

D. 3

E. 4

$$8^(1/2)$$ = 2.83

Putting values of x in 4^x

if x=1/2, 4^x = 2
If x=1, 4^x=4
if x=2, 4^x = 16

Closest value is 2 hence A

Please correct me if i am wrong

Let me correct myself

$$8^{(\frac{1}{2})} = 4^x$$
We can write it as
64^(2/2) = 64^(x/3)

x/3 = 1
x=3
Hence option D

mynamegoeson
$$8^{(\frac{1}{2})}$$ is not equal to 64^(2/2) . it is equal to 64^(1/4)
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/4

B. 2/3

C. 3/4

D. 4/3

E. 1

Apologise to all of you. Copied options of another question here. Edited.
_________________
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

Bunuel wrote:
Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/4

B. 2/3

C. 3/4

D. 4/3

E. 1

Apologise to all of you. Copied options of another question here. Edited.

No issues Bunuel .. You are doing great work.. You have posted so many questions on daily basis. So sometimes you might get confused with options.. Humans But your work is helping us a lot in preparation of Quant. Keep up the good work..
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3344
Location: India
GPA: 3.12
If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

Since $$8^{(\frac{1}{2})} = 2*\sqrt{2}$$

We have to find which value of x makes $$4^x = 2*\sqrt{2}$$

Of the available options, $$x=\frac{3}{4}$$(Option C) makes

$$4^x = 4^{\frac{3}{4}} = (4*4*4)^{\frac{1}{4}} = 2*\sqrt{2} = 8^{(\frac{1}{2})}$$
_________________
You've got what it takes, but it will take everything you've got
Senior Manager  B
Joined: 28 Jun 2015
Posts: 283
Concentration: Finance
GPA: 3.5
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

$$8^{\frac{1}{2}} = 4^{x}$$

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

$$2x = \frac{3}{2}$$

$$x = \frac{3}{4}$$. Ans - C.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

Bunuel wrote:
If $$8^{(\frac{1}{2})} = 4^x$$, what is the value of x?

A. 1/4

B. 2/3

C. 3/4

D. 4/3

E. 1

Lets simplify the given equation and determine x:

8^(½) = 4^x

(2^3)^½ = 2^2x

2^3/2 = 2^2x

3/2 = 2x

x = 3/4

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 13168
Re: If 8^(1/2) = 4^x, what is the value of x?  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If 8^(1/2) = 4^x, what is the value of x?   [#permalink] 05 Feb 2019, 07:25
Display posts from previous: Sort by

If 8^(1/2) = 4^x, what is the value of x?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  