Exponents

For students of class 6-8 (age 12 to 14)
Naheed
Posts:20
Joined:Sun Dec 16, 2012 11:10 pm
Exponents

Unread post by Naheed » Mon Jan 05, 2015 11:54 pm

How many (a,b)s are there such that a^b= 1024 ?
Last edited by Naheed on Tue Jan 06, 2015 4:00 pm, edited 1 time in total.

tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh

Re: Exponenents

Unread post by tanmoy » Tue Jan 06, 2015 12:19 pm

$1024=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2
=2^{10}
=(2^{2})^{5}=4^{5}
=(2^{5})^{2}=32^{2}$
$\therefore (a,b)=(2,10),(4,5),(32,2)$
$\therefore$ There are $3 (a,b)s$ such that $a^{b}=1024$. :)
"Questions we can't answer are far better than answers we can't question"

Naheed
Posts:20
Joined:Sun Dec 16, 2012 11:10 pm

Re: Exponenents

Unread post by Naheed » Tue Jan 06, 2015 3:58 pm

Thanks for the solution.

Abdul Muhaimin Adeeb
Posts:1
Joined:Tue Jan 19, 2016 8:20 am

Re: Exponents

Unread post by Abdul Muhaimin Adeeb » Sat Feb 13, 2016 8:59 pm

I think answer 4.
(a,b)=(2,10),(4,5),(32,2),(1024,1).

SMMamun
Posts:57
Joined:Thu Jan 20, 2011 6:57 pm

Re: Exponents

Unread post by SMMamun » Tue Feb 16, 2016 3:19 pm

It's essential to clarify all the constraints of a problem precisely. Why should we not consider negative and fractional values for a and b for this problem? For example, what's wrong with
$(a, b)=(-2, 10), (-32, 2), (1048576, \frac{1}{2})$?

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