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

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

What is the value of x
Director
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 [#permalink] New post 25 Jan 2005, 19:02
[ (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
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 [#permalink] New post 25 Jan 2005, 21:09
I like your approach but I probably would have back solved it if I had to.

Thanks
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 [#permalink] New post 26 Jan 2005, 17:48
nocilis could you plz explain how you got

x^x^x as x^x^2

4^4 cannot be 4^2?????????????
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 [#permalink] New post 26 Jan 2005, 19:39
Vijo:
I have expanded [ (x)^x]^x and not x^x^x to x^(x^2)
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 [#permalink] New post 27 Jan 2005, 05:41
Nocilis

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

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Vijo.
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 [#permalink] New post 27 Jan 2005, 08:14
(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)
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 [#permalink] New post 27 Jan 2005, 08:42
I loved this question. Learn the exponent properties as it could very likely be tested on the GMAT.
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Best Regards,

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  [#permalink] 27 Jan 2005, 08:42
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