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

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

by Brent@GMATPrepNow » Thu Aug 20, 2020 7:55 am
BTGModeratorVI wrote: ↑
Thu Aug 20, 2020 7:19 am
 What is the smallest integer x for which 81^x > 3^24?

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

Answer: B
Source: Veritas Prep
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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