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# What is the least integer p for which 27^p > 3^18?

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Math Expert
Joined: 02 Sep 2009
Posts: 58312
What is the least integer p for which 27^p > 3^18?  [#permalink]

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21 Mar 2018, 23:07
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5% (low)

Question Stats:

86% (00:29) correct 14% (00:42) wrong based on 76 sessions

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What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

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Joined: 14 Mar 2018
Posts: 10
Re: What is the least integer p for which 27^p > 3^18?  [#permalink]

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21 Mar 2018, 23:11
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

3^3p > 3^18
p>6
p=7
B
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What is the least integer p for which 27^p > 3^18?  [#permalink]

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21 Mar 2018, 23:15
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

$$27^p$$ can be simplified as $$(3^3)^p = 3^{3p}$$ because$$(a^m)^n = a^{m*n}$$

$$3^{3p} > 3^{18}$$ -> $$3p > 18$$ -> $$p > 6$$

Therefore, the least value of p for which $$27^p > 3^{18}$$ is 7 (Option B)
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What is the least integer p for which 27^p > 3^18?  [#permalink]

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22 Mar 2018, 01:41

Solution

We need to find the smallest integer p for which $$27^p >3^{18}$$.

Working out:

• $$27^p >3^{18}$$

• $$(3^3)^p > 3^{18}$$

• By applying $${(a^m)}^n = a^{m*n}$$, we get $$3^{3p} > 3^{18}$$

• Hence, $$3p> 18$$.
o $$p>6.$$

• Hence, the smallest integer value of $$p$$ greater than $$6$$ is 7.

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Re: What is the least integer p for which 27^p > 3^18?  [#permalink]

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23 Mar 2018, 10:16
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

$$27^p > 3^{18}$$

$$3^3p > 3^{18}$$

3p > 18.....p>6

Least integer power is 7

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Posts: 2817
Re: What is the least integer p for which 27^p > 3^18?  [#permalink]

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23 Mar 2018, 12:41
Bunuel wrote:
What is the least integer p for which $$27^p > 3^{18}$$?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 18

We first re-express 27 as 3^3, and so 27^p = (3^3)^p = 3^3p. Simplifying the inequality, we have:

27^p > 3^18

3^3p > 3^18

3p > 18

p > 6

The least integer greater than 6 is 7.

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Re: What is the least integer p for which 27^p > 3^18?   [#permalink] 23 Mar 2018, 12:41
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