NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 10:41 It is currently 26 Apr 2024, 10:41
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 x=100^100, x^x=10^k, k=

User avatar
young_gun
Current Student
Joined: 31 Aug 2007
Posts: 283
Own Kudos [?]: 623 [0]
Given Kudos: 1
Send PM
If x=100^100, x^x=10^k, k= [#permalink] New post   01 Oct 2007, 13:56
If x=100^100, x^x=10^k, k=?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
12345678
Manager
Manager
Joined: 09 Jul 2007
Posts: 84
Own Kudos [?]: 599 [0]
Given Kudos: 0
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   01 Oct 2007, 14:07
K=100000

x^x=100^100^100

=100^10000

=10^100000

so k=100000
User avatar
StartupAddict
Senior Manager
Senior Manager
Joined: 31 Mar 2007
Posts: 364
Own Kudos [?]: 182 [0]
Given Kudos: 0
Location: Canada eh
 Q50  V41
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   01 Oct 2007, 14:35
k = 2 * 10^202

how the hell did you get 10 000 lol

x^x = (100^100)^(100^100)
User avatar
IrinaOK
Senior Manager
Senior Manager
Joined: 22 Aug 2007
Posts: 276
Own Kudos [?]: 465 [0]
Given Kudos: 0
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   01 Oct 2007, 14:38
young_gun wrote:
If x=100^100, x^x=10^k, k=?


X=100^100=10^2*100=10^200

X^X=10^200^(10^200)=10^(200*10^200)=10^(2*10^2*10^200)=
10^ 2*10^202

10^ 2*10^202=10^K

K=2*10^202
User avatar
12345678
Manager
Manager
Joined: 09 Jul 2007
Posts: 84
Own Kudos [?]: 599 [0]
Given Kudos: 0
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   01 Oct 2007, 14:42
StartupAddict wrote:
k = 2 * 10^202

how the hell did you get 10 000 lol

x^x = (100^100)^(100^100)


arghhh again a careless mistake..its already 3am..my brain is completely dead! i better go to sleep..
User avatar
Ravshonbek
Director
Director
Joined: 09 Jul 2007
Posts: 568
Own Kudos [?]: 552 [0]
Given Kudos: 0
Location: London
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   01 Oct 2007, 15:42
young_gun wrote:
If x=100^100, x^x=10^k, k=?


x=100^100 ----> x=10^200
x^x=10^k -----> x=10^(k/x)

x=x

10^(k/x)=10^200, drop the bases

k/x=200
k=200*x ----->k=2*10^2*10^200 -----> k=2*10^202=2*100^101
avatar
slsu
Intern
Intern
Joined: 28 Aug 2007
Posts: 9
Own Kudos [?]: 64 [0]
Given Kudos: 0
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   02 Oct 2007, 12:23
Hi,

Can you explain how you got from x^x=10^k -----> x=10^(k/x)?
User avatar
young_gun
Current Student
Joined: 31 Aug 2007
Posts: 283
Own Kudos [?]: 623 [0]
Given Kudos: 1
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   02 Oct 2007, 13:15
slsu wrote:
Hi,

Can you explain how you got from x^x=10^k -----> x=10^(k/x)?


Sure, it's just a way to isolate x.

x^(x)(1/x)=x, apply the 1/x power to both sides...
User avatar
Ravshonbek
Director
Director
Joined: 09 Jul 2007
Posts: 568
Own Kudos [?]: 552 [0]
Given Kudos: 0
Location: London
Send PM
Re: If x=100^100, x^x=10^k, k= [#permalink] New post   02 Oct 2007, 13:19
slsu wrote:
Hi,

Can you explain how you got from x^x=10^k -----> x=10^(k/x)?


x=10^(k/x)
x=10^200
x=x
10^(k/x)=10^200
drop the bases

k/x=200
k=200x then bring x back



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: If x=100^100, x^x=10^k, k= [#permalink]
02 Oct 2007, 13:19
Moderator:
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