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If x^9 = 9^9^9, what is the value of x?

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If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 30 Jul 2019, 08:50
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A
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D
E

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If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 30 Jul 2019, 21:50
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x^9 = 9^(9^9)

To simplify understanding :

x^9 = 9^(9*9*9*9*9*9*9*9*9)

Taking L.H.S's power of 9 to the right side of the equation For example : [x^2 = 4 => square Root of 4 or 4^(1/2)]

x = 9^(9*9*9*9*9*9*9*9*9/9)

=> x = 9^(9*9*9*9*9*9*9*9) => 9^(9^8)

Ans : D
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Re: If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 30 Jul 2019, 09:33
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suchita2409 wrote:
x^9 = 9^9^9
x=9^9
B

Posted from my mobile device



Please see that (a^m)^n= a^m*n
Replacing x by 9^9 would mean (9^9)^9= 9^81

See that the number in question is much larger.
(9^9^8)^9= 9^9^8*9= 9^9^9

Answer D
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If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 30 Jul 2019, 21:29
vinayakvaish wrote:
suchita2409 wrote:
x^9 = 9^9^9
x=9^9
B

Posted from my mobile device



Please see that (a^m)^n= a^m*n
Replacing x by 9^9 would mean (9^9)^9= 9^81

See that the number in question is much larger.
(9^9^8)^9= 9^9^8*9= 9^9^9

Answer D


Am unable to understand this explanation. Can someone explain it once again. Tia.
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Re: If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 05 Aug 2019, 19:14
Bunuel wrote:
If \(x^9 = 9^{9^9}\), what is the value of \(x\)?


A. \(9^8\)

B. \(9^9\)

C. \(9^{8^9}\)

D. \(9^{9^8}\)

E. \(9^{9^9}\)


Note that 9^9^9 is NOT the same as (9^9)^9 = 9^81. It is, instead, 9^(9^9), which is a much greater number than (9^9)^9.

Let’s take the 9th root of each side or rather, let’s raise each side to the power of 1/9:

(x^9)^(1/9) = [9^(9^9)]^(1/9)

x = 9^((9^9)*(1/9))

Since 1/9 = 9^(-1), we have:

x = 9^((9^9)*(9^(-1)))

x = 9^(9^(9 + (-1)))

x = 9^(9^8)

Answer: D
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Re: If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 05 Aug 2019, 20:49
Hello Can someone clarify one point for me please ?
Does :
(x^a)^b = x^(a*b) ?

x^a^b = x^(a*a*a*...*a) for example if b = 4 -> x^(a*a*a*a) ?

Thank you
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Re: If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 06 Aug 2019, 01:03
1
Coggi wrote:
Hello Can someone clarify one point for me please ?
Does :
(x^a)^b = x^(a*b) ?

x^a^b = x^(a*a*a*...*a) for example if b = 4 -> x^(a*a*a*a) ?

Thank you


(x^a)^b = x^(a*b)

But x^a^b is not = (x^a)^b

It starts from the top ... For example x^a^b^c^d^e will start from solving d^e then c^d^e then b^c^d^e and so on.

2^3^4 = 2^81

Whereas (2^3)^4 = 8^4 which is completely different.

Hope this clarifies your doubt.
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Re: If x^9 = 9^9^9, what is the value of x?  [#permalink]

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New post 06 Aug 2019, 01:16
Solution is attached

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Re: If x^9 = 9^9^9, what is the value of x?   [#permalink] 06 Aug 2019, 01:16
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