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

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If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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New post 15 Oct 2011, 12:26
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If \(2^x-2^{(x-2)}=3*2^{13}\) what is the value of x?

A. 9
B. 11
C. 13
D. 15
E. 17

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2-x-2-x-2-3-2-13-what-is-the-value-of-x-130109.html
[Reveal] Spoiler: OA
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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New post 15 Oct 2011, 13:43
danielezunino wrote:
Hello,

can anybody help me understand this question?

Many thanks!!
Daniele


If 2^x- 2^(x-2) = 3(2^13) then x is equal to ?
a .9
b.11
c.13
d.15
e.17



Q:2^x- 2^(x-2) = 3(2^13)


==>2^x = 3(2^13)+2^(x-2)

So the value of X should be more than 13. Only 2 options which are greater than 13.

15 and 17

If we substitute 15.

2^15 = 3(2^13)+2^13
2^2 * 2^13 = 4(2^13)
4(2^13) = 4 (2^13) so 15 (D )
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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New post 15 Oct 2011, 13:52
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gopu106 wrote:
danielezunino wrote:
Hello,

can anybody help me understand this question?

Many thanks!!
Daniele


If 2^x- 2^(x-2) = 3(2^13) then x is equal to ?
a .9
b.11
c.13
d.15
e.17



Q:2^x- 2^(x-2) = 3(2^13)


==>2^x = 3(2^13)+2^(x-2)

So the value of X should be more than 13. Only 2 options which are greater than 13.

15 and 17

If we substitute 15.

2^15 = 3(2^13)+2^13
2^2 * 2^13 = 4(2^13)
4(2^13) = 4 (2^13) so 15 (D )


Another way

Q:2^x- 2^(x-2) = 3(2^13)

==>[2^2 * 2^(x-2)] - 2^(x-2) = 3(2^13)
==>4[2^(x-2)] - 2^(x-2) = 3(2^13)
==>3[2^(x-2)] = 3(2^13)

==>x-2 = 13
x=15 (D)
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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New post 15 Oct 2011, 23:35
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Let us take 2^x =a

now in the equation we replace 2^x by a
=> a-a/4 = 3(2^13)
=>a/4=2^13
=>a=2^15

now a=2^x =>2^x = 2^15

so x=15
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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New post 16 Oct 2011, 01:13
Thanks a lot to both of you!!! now it is really clear :-D
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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New post 27 Mar 2016, 17:46
subhajeet wrote:
Let us take 2^x =a

now in the equation we replace 2^x by a
=> a-a/4 = 3(2^13)
=>a/4=2^13
=>a=2^15

now a=2^x =>2^x = 2^15

so x=15


How do you take 2^(x-2) as a/4?Can you explain please
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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New post 28 Mar 2016, 02:06
Expert's post
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theperfectgentleman wrote:
subhajeet wrote:
Let us take 2^x =a

now in the equation we replace 2^x by a
=> a-a/4 = 3(2^13)
=>a/4=2^13
=>a=2^15

now a=2^x =>2^x = 2^15

so x=15


How do you take 2^(x-2) as a/4?Can you explain please


\(2^{x-2} = 2^x*2^{-2}=\frac{2^x}{4}=\frac{a}{4}\)

If \(2^x-2^{x-2}=3*2^{13}\) what is the value of x?
A. 9
B. 11
C. 13
D. 15
E. 17

\(2^x-2^{x-2}=3*2^{13}\) --> \(2^x-2^{x}*2^{-2}=3*2^{13}\) --> \(2^x-\frac{2^{x}}{2^{2}}=3*2^{13}\) --> \(2^x(1-\frac{1}{2^{2}})=3*2^{13}\) --> \(2^x*\frac{3}{2^{2}}=3*2^{13}\) --> \(2^x=2^{15}\) --> \(x=15\).

Answer: D.

Hope it's clear.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2-x-2-x-2-3-2-13-what-is-the-value-of-x-130109.html
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?   [#permalink] 28 Mar 2016, 02:06
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