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# What is the smallest integer a for which 27^a>3^24?

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What is the smallest integer a for which 27^a>3^24?  [#permalink]

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29 Feb 2016, 11:06
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83% (00:40) correct 17% (00:38) wrong based on 160 sessions

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What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12

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Re: What is the smallest integer a for which 27^a>3^24?  [#permalink]

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29 Feb 2016, 11:43
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12

27= 3^3
hence, (3^3)^a
Option C would make it 3^27 > 3^24
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Re: What is the smallest integer a for which 27^a>3^24?  [#permalink]

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03 Mar 2016, 03:12
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12

27^a > 3^24
Converting into the same bases:
27^a > 27^8
Therefore for the equation to hold true, a > 8 or a = 9
Option C
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What is the smallest integer a for which 27^a>3^24?  [#permalink]

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03 Mar 2016, 18:10
Simply and how else is there to do so then:
$$3^{3a} > 3^{24}$$
$$3a > 24$$
$$a > 8$$

Therefore, the smallest integer is 9.

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Re: What is the smallest integer a for which 27^a>3^24?  [#permalink]

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09 Mar 2016, 23:43
Nice Question..
Here just need to write 27 as 3^3 and we are able to see that a must be atleast 9
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Re: What is the smallest integer a for which 27^a>3^24?  [#permalink]

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21 Mar 2018, 03:21
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12

$$27^a > 3^{24}$$

or, $$3^{3a} > 3^{24}$$

when "a" = 9

$$3^{3*9} > 3^{24}$$

$$3^{27} > 3^{24}$$

Hence (B)
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Re: What is the smallest integer a for which 27^a>3^24?  [#permalink]

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22 Mar 2018, 15:44
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12

Re-expressing 27 as 3^3, we have:

3^3a > 3^24

When bases are equal, we can deal with just the exponents, as follows:

3a > 24

a > 8

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Re: What is the smallest integer a for which 27^a>3^24?  [#permalink]

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26 Mar 2018, 10:52

Solution:

Given:

• a is an integer.

• $$27^a > 3^{24}$$.

Working out:

We need to find the smallest value of the integer “a”.

The given inequality is $$27^a >3^{24}$$

$$27^a$$ can be written as $$(3^3)^a$$

So, our inequality now becomes: $$3^3a > 3^{24}$$

• Since the bases are same, we can equate the exponents.

• Thus, $$3a> 24$$

• Or, $$a>8$$

The smallest integer greater than 8 is 9, and hence $$a =9$$

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Re: What is the smallest integer a for which 27^a>3^24?   [#permalink] 26 Mar 2018, 10:52
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