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# x)^x]^x = 3*3^1/2 What is the value of x

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Director
Joined: 07 Jun 2004
Posts: 614
Location: PA
Followers: 3

Kudos [?]: 267 [0], given: 22

x)^x]^x = 3*3^1/2 What is the value of x [#permalink]  25 Jan 2005, 18:21
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[ (x)^x]^x = 3*3^1/2

What is the value of x
Director
Joined: 19 Nov 2004
Posts: 563
Location: SF Bay Area, USA
Followers: 3

Kudos [?]: 57 [0], given: 0

[ (x)^x]^x = 3*3^1/2

x^(x^2)= 3^1/2* 3^1/2 * 3 ^1/2
= (3^1/2) ^3
= (3^1/2)^ (3^1/2)^2

=> x = 3^1/2
Director
Joined: 25 Jan 2004
Posts: 728
Location: Milwaukee
Followers: 2

Kudos [?]: 12 [0], given: 0

I like your approach but I probably would have back solved it if I had to.

Thanks
_________________

Praveen

Manager
Joined: 01 Jan 2005
Posts: 167
Location: NJ
Followers: 1

Kudos [?]: 0 [0], given: 0

nocilis could you plz explain how you got

x^x^x as x^x^2

4^4 cannot be 4^2?????????????
Director
Joined: 19 Nov 2004
Posts: 563
Location: SF Bay Area, USA
Followers: 3

Kudos [?]: 57 [0], given: 0

Vijo:
I have expanded [ (x)^x]^x and not x^x^x to x^(x^2)
Manager
Joined: 01 Jan 2005
Posts: 167
Location: NJ
Followers: 1

Kudos [?]: 0 [0], given: 0

Nocilis

I really cannot understand this plz expain...... how did you expand. It wud be great if you could write explaination.

Thanks,
Vijo.
SVP
Joined: 03 Jan 2005
Posts: 2250
Followers: 13

Kudos [?]: 216 [0], given: 0

(x^a)^b=x^(a*b)
For example, (2^2)^3=2^6

So in our case
(x^x)^x=x^(x*x)=x^(x^2)
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4313
Followers: 26

Kudos [?]: 214 [0], given: 0

I loved this question. Learn the exponent properties as it could very likely be tested on the GMAT.
_________________

Best Regards,

Paul

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