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Status: booyeh!
Joined: 26 May 2017
Posts: 15
Location: India
Concentration: Strategy, Marketing
If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 60% (01:42) correct 40% (01:45) wrong based on 136 sessions

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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. $$81^{2}$$
Manager  G
Joined: 29 Nov 2018
Posts: 84
Location: India
GPA: 4
WE: Information Technology (Consulting)
Re: If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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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

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Mofe Bhatia
Senior Manager  P
Joined: 31 May 2017
Posts: 412
If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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2
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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Intern  S
Joined: 30 May 2017
Posts: 42
Location: India
Concentration: Finance, Strategy
Schools: Wharton, IESE, ISB, NUS
GPA: 4
WE: Engineering (Consulting)
Re: If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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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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Intern  B
Joined: 13 Mar 2019
Posts: 27
Re: If a=3^9 and a^a=3^b, what is the value of b?  [#permalink]

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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. Re: If a=3^9 and a^a=3^b, what is the value of b?   [#permalink] 08 Aug 2019, 10:05

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