NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 00:06 It is currently 26 Apr 2024, 00:06
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619076 [3]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   Updated on: 22 Jun 2017, 07:49
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

79% (00:53) correct 21% (01:11) wrong based on 107 sessions
Hide Show 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
ShowHide Answer
Official Answer
C

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.
User avatar
L
sashiim20
Director
Director
Joined: 04 Dec 2015
Posts: 620
Own Kudos [?]: 1585 [1]
Given Kudos: 276
Location: India
Concentration: Technology, Strategy
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User
If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   Updated on: 22 Jun 2017, 08:04
1
Bookmarks
\(8^{(\frac{1}{2})} = 4^x\)

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

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

\(x = \frac{3}{4}\) . 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.
User avatar
P
Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Posts: 531
Own Kudos [?]: 577 [0]
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Send PM
GMAT ToolKit User Reviews Badge
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 06:24
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
avatar
B
amastu
Intern
Intern
Joined: 29 Mar 2016
Posts: 5
Own Kudos [?]: 2 [1]
Given Kudos: 3
Location: United States
Schools: Stern '20
GMAT 1: 720 Q48 V41
GPA: 3
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 06:30
1
Kudos
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?
User avatar
P
Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Posts: 531
Own Kudos [?]: 577 [1]
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Send PM
GMAT ToolKit User Reviews Badge
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   Updated on: 22 Jun 2017, 06:53
1
Kudos
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

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.
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 628
Own Kudos [?]: 589 [1]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 06:42
1
Kudos
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...
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 628
Own Kudos [?]: 589 [1]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 06:43
1
Kudos
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
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29936 [1]
Given Kudos: 799
Location: Canada
Send PM
If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   Updated on: 28 May 2020, 09:27
1
Kudos
Expert Reply
Top Contributor
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


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

Answer: C

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 22 Jun 2017, 06:44.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:27, edited 1 time in total.
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 628
Own Kudos [?]: 589 [0]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 06:46
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...
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 628
Own Kudos [?]: 589 [0]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 06:49
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)
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619076 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 07:53
Expert Reply
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.
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 628
Own Kudos [?]: 589 [0]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 08:05
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..
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5206 [0]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 09:02
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

\(4^x = 4^{\frac{3}{4}} = (4*4*4)^{\frac{1}{4}} = 2*\sqrt{2} = 8^{(\frac{1}{2})}\)
User avatar
B
TimeTraveller
Senior Manager
Senior Manager
Joined: 28 Jun 2015
Posts: 250
Own Kudos [?]: 293 [0]
Given Kudos: 47
Concentration: Finance
GPA: 3.5
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   22 Jun 2017, 09:23
\(8^{\frac{1}{2}} = 4^{x}\)

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

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

\(x = \frac{3}{4}\). Ans - C.
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6275 [0]
Given Kudos: 1646
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   24 Jun 2017, 08:30
Expert Reply
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

Answer: C
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32680
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink] New post   07 Aug 2023, 04:32
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.
GMAT Club Bot
gmatclubot
Re: If 8^(1/2) = 4^x, what is the value of x? [#permalink]
07 Aug 2023, 04:32
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions