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Bunuel
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What is the smallest integer x for which 81^x >3^24? 01 Mar 2017, 05:38
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80% (00:41) correct 20% (00:57) wrong based on 222 sessions

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What is the smallest integer x for which 81^x >3^24?

A. 6
B. 7
C. 8
D. 10
E. 24
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B
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What is the smallest integer x for which 81^x >3^24? Updated on: 28 May 2020, 09:28
Originally posted by BrentGMATPrepNow on 01 Mar 2017, 06:01.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:28, edited 1 time in total.
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Bunuel
What is the smallest integer x for which \(81^x > 3^{24}\)?

A. 6
B. 7
C. 8
D. 10
E. 24
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Given: 81^x > 24
Rewrite 81 with base 3 to get: (3^4)^x > 3^24
Apply power of a power law to get: 3^(4x) > 3^24
Since the bases are the same, we can conclude that 4x > 24
Divide both sides by 4 to get: x > 6

Since we're told that x is an integer, we can conclude that 7 is the smallest value of x that satisfies this inequality.
Answer: B

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What is the smallest integer x for which 81^x >3^24? 01 Mar 2017, 06:04
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Bunuel
What is the smallest integer x for which 81^x >3^24?

A. 6
B. 7
C. 8
D. 10
E. 24
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HI

81^x >3^24==>3^4x>3^24

To be true x=7

Hence B
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What is the smallest integer x for which 81^x >3^24? 01 Mar 2017, 12:02
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Bunuel
What is the smallest integer x for which 81^x >3^24?

A. 6
B. 7
C. 8
D. 10
E. 24
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81^x >3^24

= 3^4x >3^24

Or, 4x > 24

So, x > 6

Thus, the smallest integer x will be 7

Answer will be (B) 7
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What is the smallest integer x for which 81^x >3^24? 01 Mar 2017, 22:54
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\(81^x\)> \(3^{24}\)
\((3^4)^x > 3^{24}\)
\(3^{4x} > 3^{24}\)

Hence, x = 7, Answer B
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What is the smallest integer x for which 81^x >3^24? 02 Mar 2017, 18:40
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Bunuel
What is the smallest integer x for which 81^x >3^24?

A. 6
B. 7
C. 8
D. 10
E. 24
Show more


Since 81 = 3^4, we can rewrite the given inequality as:

3^(4x) > 3^24

When the bases of an exponential equation are equal, we can relate the exponents:.

4x > 24

x > 6

Thus, the smallest integer is 7.

Answer: B
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What is the smallest integer x for which 81^x >3^24? 14 Apr 2021, 05:24
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