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# What is the largest integer k for which 4^k < 64^15 ?

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Intern
Joined: 21 Apr 2018
Posts: 8
What is the largest integer k for which 4^k < 64^15 ? [#permalink]

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Updated on: 30 Apr 2018, 22:04
00:00

Difficulty:

15% (low)

Question Stats:

84% (00:34) correct 16% (01:08) wrong based on 25 sessions

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What is the largest integer k for which 4^k < 64^15 ?

A. 59
B. 46
C. 45
D. 44
E. 14

Originally posted by Ashishkakkar2189 on 30 Apr 2018, 21:58.
Last edited by Bunuel on 30 Apr 2018, 22:04, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Math Expert
Joined: 02 Sep 2009
Posts: 45302
Re: What is the largest integer k for which 4^k < 64^15 ? [#permalink]

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30 Apr 2018, 22:07
Ashishkakkar2189 wrote:
What is the largest integer k for which 4^k < 64^15 ?

A. 59
B. 46
C. 45
D. 44
E. 14

$$4^k < 64^{15}$$;

$$4^k < (4^3)^{15}$$;

$$4^k < 4^{45}$$.

The largest integer k for which the above holds true is 44.

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Re: What is the largest integer k for which 4^k < 64^15 ?   [#permalink] 30 Apr 2018, 22:07
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