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which of the following has the maximum value? a) 5^15 b) 6^14 c) 3^21 d) 2^30 PLEASE EXPLAIN :)

which of the following has the maximum value?
a) 5^15
b) 6^14
c) 3^21
d) 2^30

PLEASE EXPLAIN :)  

Grade:10

3 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Amin,

See 2^30 = (2^2)^15 = 4^15.... so < 5^15.

Next consider 3^21 = (3^3)^7=27^7

where as 6^14 is (6^2)^7 = 36^7

So 3^21<6^14.

 

Between 5^15, and 6^14.

Now consider (6/5)^14 = (1.2)^14 which is greater than (1.2)^12 = (1.2^4)^3

Now 1.2^4>2

so 1.2^12>8

 

So clearly (6/5)^14>5

so 6^14/5^14>5

So 6^14>5^15.

 

Hence 6^14 is the greatest.

 

All the best.

Regards,

Ashwin (IIT Madras).

Sathya
35 Points
9 years ago

I think b is the correct option .The reason is 6^21 can be written as 2^21 x 3^21.It is greater than c and d for sure,the left one is option a.option a is surely lesser than b(as u can see).So b is the answer.Please post these type of questions,i will be ready to answer.

Sathya
35 Points
9 years ago

I think so option b is the right answer.Is it correct?If yes,ill explain to you

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