If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

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by ajith » Tue Feb 02, 2010 9:31 am
bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

A.12
B.14
C.15
D.17
E.19
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2)

x-2 =13

x =15
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by thephoenix » Tue Feb 02, 2010 9:34 am
2^x - 2^x-2 = 3*(2)^13

2^x - 2^x-2=2^x-2^x/2^2=2^x(1-1/4)=2^x*(3/4)=3*2^x-2--->x-2=13--->x=15

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by harshavardhanc » Tue Feb 02, 2010 9:48 am
you can go through all the lengthy calculation and arrive at the answer. No one will get this question wrong. definitely! Everyone knows how to solve a linear equation and knows powers of 2.

But, I think this question can be a boon or a bane ? it totally depends on you.

You spend at 3 mins in making an equation and then solve it.


Or

you can see 3 as (2^2 - 1 ) and save at least 2 mins ! that's 2 extra minutes!


Now the R.H.S becomes 2^13 * ( 2^2 -1 ) = 2^15 - 2^13 ( looks like L.H.S ? )

Pick your X !
Regards,
Harsha

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by ajith » Tue Feb 02, 2010 9:53 am
harshavardhanc wrote:you can go through all the lengthy calculation and arrive at the answer. No one will get this question wrong. definitely! Everyone knows how to solve a linear equation and knows powers of 2.

But, I think this question can be a boon or a bane ? it totally depends on you.

You spend at 3 mins in making an equation and then solve it.


Or

you can see 3 as (2^2 - 1 ) and save at least 2 mins ! that's 2 extra minutes!


Now the R.H.S becomes 2^13 * ( 2^2 -1 ) = 2^15 - 2^13 ( looks like L.H.S ? )

Pick your X !
Sources for the time statistics please! This problem can be done in less than 45 seconds in equation method

in this case at least the equation method is fool proof and better than non-scientific methods
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by harshavardhanc » Tue Feb 02, 2010 10:29 am
Sources for the time statistics please!
--> oh, so you ARE practicing CR as well. Good! Keep it up !
This problem can be done in less than 45 seconds in equation method
-- > Sooooooper!!!
in this case at least the equation method is fool proof and better than non-scientific methods


--> non-scientific???? did you mean non-conventional ? Then yes, my method was non-conventional.

Scientific????? I still did not understand how a scientific formula is used in the a Math problem? was it used in the solve-by-equation method? I may have missed that ! sorry again! ;)

No offenses dude! But, if you're hurt because I questioned you're method of solving, then please accept my apology! ;)

But, GMAC knows that we have a habit of starting from the "given" or the "L.H.S", and use the info to arrive at the answer.

This question, I think, is the same trap, wanting us do what we normally do.

My point was, why not take a different path and start with the numbers here and make it look like the part which has variables?

You said that it will take 45 seconds to make an eq and solve it. You surely must have done it within that time, but slow-heads like me will take more than 45 secs to solve an eq. That's how we were made by the almighty! :(

Anyway, we now have two methods to solve this question. Fellow forum-mates can choose their pick .
Regards,
Harsha

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by ajith » Tue Feb 02, 2010 10:49 am
I think problem was too straight forward to try anything unconventional. I have nothing against the unconventional methods and I am all for those.

Having said that, I do not want to get into arguments. There is nothing personal in here and I do not want to offend anybody
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by bhumika.k.shah » Wed Feb 03, 2010 7:31 am
ajith,
i got it so far. kindly explain how u got the part in bold???
ajith wrote:
bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

A.12
B.14
C.15
D.17
E.19
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2)

x-2 =13


x =15

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by armaan700+ » Wed Feb 03, 2010 7:44 am
bhumika.k.shah wrote:ajith,
i got it so far. kindly explain how u got the part in bold???
ajith wrote:
bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

A.12
B.14
C.15
D.17
E.19
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2)

x-2 =13


x =15
just compare RHS and LHS

3*2^15=3*2^(x-2)
property of exponents
if n^k*m^l=n^a*m^b
then k=a
and l=b
hence x-2=15

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by ajith » Wed Feb 03, 2010 7:45 am
bhumika.k.shah wrote:ajith,
i got it so far. kindly explain how u got the part in bold???
ajith wrote:
bhumika.k.shah wrote:
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) =

3* 2^x/4 = 3*2^x/2^2 =3*2^(x-2) [a^m/a^n = a^(m-n) ] = 3*(2)^13

3*2^(x-2)= 3*(2)^13

2^(x-2) = (2)^13

Now, x-2 = 13 [if a^x = a^y, x=y]


x =15
Hope that Helps, see the colored part
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by thephoenix » Wed Feb 03, 2010 7:47 am
armaan700+ wrote:
bhumika.k.shah wrote:ajith,
i got it so far. kindly explain how u got the part in bold???
ajith wrote:
bhumika.k.shah wrote:If 2^x - 2^x-2 = 3*(2)^13, What is the value of x?

A.12
B.14
C.15
D.17
E.19
2^x - 2^x/4 = 2^x(1-1/4) = 2^x(3/4) = 3*2^(x-2)

x-2 =13


x =15

just compare RHS and LHS

3*2^15=3*2^(x-2)
property of exponents
if n^k*m^l=n^a*m^b
then k=a
and l=b
hence x-2=15
in exponents
a^x=b*y---->x=y

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by bhumika.k.shah » Wed Feb 03, 2010 7:54 am
YES IT DID :D

Any good link for exponents and roots ..???
ajith wrote: Hope that Helps

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by ajith » Wed Feb 03, 2010 7:59 am
bhumika.k.shah wrote:YES IT DID :D

Any good link for exponents and roots ..???
ajith wrote: Hope that Helps
https://www.mathsisfun.com/algebra/expo ... s.html
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