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If a=3^9 and a^a=3^b, what is the value of b?

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If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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New post 18 May 2019, 09:56
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Question Stats:

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If a=\(3^{9}\) and \(a^{a}\)=\(3^{b}\), what is the value of b?

A. \(3^{12}\)
B. \(3^{11}\)
C. 27
D. 243
E. \(81^{2}\)
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Re: If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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New post 18 May 2019, 11:29
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pvs29 wrote:
If a=\(3^{9}\) and \(a^{a}\)=\(3^{b}\), what is the value of b?

A. \(3^{12}\)
B. \(3^{11}\)
C. 27
D. 243
E. \(81^{2}\)



a^a = 3^b
(3^9)3^9 = 3^b
3^(9*3^9) = 3^b

Equating values for b

b = 9 * 3^9
b = 3^2 * 3^9
b = 3^(9+2)
b = 3^11

Correct Answer B

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If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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New post 18 May 2019, 11:57
1
a = \(3^9\)

\(a^a\) = \(3^b\)

(3^9)^(3^9) = 3^b

This equation becomes

b = \((9*3^9)\)
b = \((3^2 * 3^9)\)
b = 3^11

Ans: B
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Re: If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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New post 06 Aug 2019, 12:21
Since a^a = 3^b
a = 3^(b/a) ------(1)
Now we know a = 3^9 ----(2)

Equating 1 and 2 we have,
3^9 = 3 ^(b/a)
Base being the same, we have
9 = b/a
b= 9*a
b= 3^2 * 3^9 (since 9 can be written as square of 3
b= 3^11 and hence the option B

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Re: If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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New post 08 Aug 2019, 11:05
1
a = 3^(9) and a ^a = 3 ^ b
Now a = 3^(b/a)
b/a = 9
b = 9.a
b = 9*3^(9)
so b = 3^11.
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Re: If a=3^9 and a^a=3^b, what is the value of b?   [#permalink] 08 Aug 2019, 11:05
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If a=3^9 and a^a=3^b, what is the value of b?

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