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If k=3^81 and k^k=3^m, what is the value of m?

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If k=3^81 and k^k=3^m, what is the value of m?  [#permalink]

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11 Jul 2018, 05:36
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62% (02:01) correct 38% (01:51) wrong based on 131 sessions

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If $$k=3^{81}$$ and $$k^k=3^m$$, what is the value of m?

A. $$85$$
B. $$24^{381}$$
C. $$3^{54}$$
D. $$3^{85}$$
E. $$3^{72}$$
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Posts: 484
Concentration: Accounting, Finance
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Re: If k=3^81 and k^k=3^m, what is the value of m?  [#permalink]

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11 Jul 2018, 06:06
Karthik200 wrote:
If $$k=3^{81}$$ and $$k^k=3^m$$, what is the value of m?

A. $$85$$
B. $$24^{381}$$
C. $$3^{54}$$
D. $$3^{85}$$
E. $$3^{72}$$

I think answer should be D. kindly verify the official answer.
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Re: If k=3^81 and k^k=3^m, what is the value of m?  [#permalink]

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11 Jul 2018, 06:18
Karthik200 wrote:
If $$k=3^{81}$$ and $$k^k=3^m$$, what is the value of m?

A. $$85$$
B. $$24^{381}$$
C. $$3^{54}$$
D. $$3^{85}$$
E. $$3^{72}$$

Looks like you got the OA wrong here. My answer comes out as D.
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Re: If k=3^81 and k^k=3^m, what is the value of m?  [#permalink]

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11 Jul 2018, 06:26
4
Karthik200 wrote:
If $$k=3^{81}$$ and $$k^k=3^m$$, what is the value of m?

A. $$85$$
B. $$24^{381}$$
C. $$3^{54}$$
D. $$3^{85}$$
E. $$3^{72}$$

Given $$k=3^{81}$$

Now, $$k^k=({3^{81}})^{3^{81}}$$=$${3^{{81}*3^{81}}}$$=$${3(^{{3^4}*3^{81}})}$$=$$3^{3^{85}}$$

Given $$k^k=3^m$$
So, $$3^m$$=$$3^{3^{85}}$$
Or, $$m=3^{85}$$

Ans. (D)

P.S:- Property used in solving this question:-$$a^m*a^n=a^{m+n} & ({a^m})^n={a}^{mn}$$
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Joined: 21 Feb 2018
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Re: If k=3^81 and k^k=3^m, what is the value of m?  [#permalink]

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11 Jul 2018, 22:23
k=3^81
k^k = 3^m
taking log in both equations, we get
log k = 81 log 3 ------ (1)
and
k*log k = m log 3 ------ (2)
Dividing (2) by (1)
k = m/81
=> m = k*81
or
m = 3^81*81
=3^85

D is the right answer
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Re: If k=3^81 and k^k=3^m, what is the value of m?  [#permalink]

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14 Jul 2018, 08:36
$$81 = 3^4$$

Using the property: $$a^n * a^m = a^{n+m}$$

$$3^4 * 3^{81} = 3^{4+81}$$ or $$3^{85}$$

Option D is the correct answer
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Re: If k=3^81 and k^k=3^m, what is the value of m?  [#permalink]

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17 Jul 2018, 16:25
Karthik200 wrote:
If $$k=3^{81}$$ and $$k^k=3^m$$, what is the value of m?

A. $$85$$
B. $$24^{381}$$
C. $$3^{54}$$
D. $$3^{85}$$
E. $$3^{72}$$

Since k = 3^81, k^k = (3^81)^(3^81) = (3^(3^4))^(3^81) = 3^[(3^4)*(3^81)] = 3^(3^85). So, m must be 3^85.

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Re: If k=3^81 and k^k=3^m, what is the value of m? &nbs [#permalink] 17 Jul 2018, 16:25
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