What is the smallest integer a for which 27^a3^24?

Question

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

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

Anigr16 · Answer

27= 3^3
hence, (3^3)^a
 Option C  would make it 3^27 > 3^24

TeamGMATIFY · Answer

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

mejia401 · Answer

Simply and how else is there to do so then:
 3^{3a} > 3^{24} 
 3a > 24 
 a > 8

Therefore, the smallest integer is 9.

C.

stonecold · Answer

Nice Question..
Here just need to write 27 as 3^3 and we are able to see that a must be atleast 9

AkshdeepS · Answer

27^a > 3^{24}

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

when "a" = 9

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

3^{27} > 3^{24}

Hence (B)

JeffTargetTestPrep · Answer

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

Answer: C

EgmatQuantExpert · Answer

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

Answer: Option C

Kinshook · Answer

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

27^a = 3^{3a} > 3^24 
3a > 24
a > 8
 a_{min} = 9

IMO C

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

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