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

It is currently 17 Oct 2018, 00:31

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.

Close

Request Expert Reply

Confirm Cancel

If 3^27^x = 27^3^x , then x is equal to

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

Hide Tags

Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 333
If 3^27^x = 27^3^x , then x is equal to  [#permalink]

Show Tags

New post 10 Mar 2017, 13:08
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (02:01) correct 39% (01:55) wrong based on 46 sessions

HideShow timer Statistics

If 3^27^x = 27^3^x , then x is equal to

A.−1

B. 1/2

C.1

D.2

E.-1/2
Senior Manager
Senior Manager
avatar
P
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
Reviews Badge
If 3^27^x = 27^3^x , then x is equal to  [#permalink]

Show Tags

New post 11 Mar 2017, 04:54
quantumliner wrote:
If 3^27^x = 27^3^x , then x is equal to

A.−1

B. 1/2

C.1

D.2

E.-1/2


I scratched my head a lot since I was rusty on these questions and had to view the answer first. I am partly convinced I have found the right path but would welcome any correction

RHS can be rewritten as

(3^3)^3^x

= 3 ^ (3.3^x)

equating powers of matching base from both LHS and RHS.

\(27^x = 3.3^x\)

27^x = 3^(x+1)

LHS can be rewritten.

(3^3)^x= 3^(x+1)

3^3x = 3^(x+1)

equating powers of matching base again

\(3x = x + 1\)

\(2x = 1\)

\(x = 1/2\)
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Intern
Intern
avatar
Joined: 13 May 2014
Posts: 5
Schools: ISB '16
GMAT ToolKit User
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

Show Tags

New post 11 Mar 2017, 07:41
You lost me while solving RHS when you stated that 27^x = 3^(x+1).

Could you please elaborate?

Sent from my SM-N910G using GMAT Club Forum mobile app
Senior Manager
Senior Manager
avatar
P
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
Reviews Badge
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

Show Tags

New post 11 Mar 2017, 07:52
On RHS, we had \(3 x 3^x\) which is same as \(3^1 x 3^x\) and when base is same we just add the powers so it becomes 3^x+1

Sent from my Redmi Note 4 using GMAT Club Forum mobile app
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Senior Manager
Senior Manager
avatar
B
Joined: 06 Dec 2016
Posts: 250
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

Show Tags

New post 11 Mar 2017, 20:23
Can VeritasPrepKarishma or Bunuel please explain this one to me step by step.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8386
Location: Pune, India
Re: If 3^27^x = 27^3^x , then x is equal to  [#permalink]

Show Tags

New post 11 Mar 2017, 21:15
1
matthewsmith_89 wrote:
Can VeritasPrepKarishma or Bunuel please explain this one to me step by step.



Here is the step by step process:

Attachment:
IMG_7211.JPG
IMG_7211.JPG [ 1.56 MiB | Viewed 1337 times ]


Note: When two numbers with the same base are multiplied, their exponents get added.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

GMAT Club Bot
Re: If 3^27^x = 27^3^x , then x is equal to &nbs [#permalink] 11 Mar 2017, 21:15
Display posts from previous: Sort by

If 3^27^x = 27^3^x , then x is equal to

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.