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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]  18 Jan 2006, 21:07
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

I can get the answer by plugging in answer choices but I would like to understand how to correctly derive the answer.

Last edited by timetrader on 18 Jun 2009, 16:04, edited 1 time in total.
Math format
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Re: exponents [#permalink]  18 Jan 2006, 21:15
vbang wrote:
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

I can get the answer by plugging in answer choices but I would like to understand how to correctly derive the answer.

2^x-2^x-2=3(2^13)
2^x-2(2^2-1)=3*2^13
2^x-2*(4-1)=3*2^13
2^x-2=2^13
x-2=13
x=15
D it is
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Re: exponents [#permalink]  18 Jan 2006, 21:25
vbang wrote:
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
I can get the answer by plugging in answer choices but I would like to understand how to correctly derive the answer.

1. (2^x) - 2^(x-2) = 3(2^13)
2. (2^x) - (2^x) -2 = 3(2^13)
3. 2^(x-2)^(x-2) = 3(2^13)
Senior Manager
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ambiguish question
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Ambiguous question. Could be interpreted inmany ways without parentheses.
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Director
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ps_dahiya wrote:
Ambiguous question. Could be interpreted inmany ways without parentheses.

Agree but this quest discussed recently so the stem should be
2^x-(2^(x-2)) = 3(2^13) Hope this helps
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1
KUDOS
2^x-(2^(x-2)) = (2^x)*[1-2^(-2)]= (2^x)*(3/4)=3* [2^x*2^(-2)]=3* [2^(x-2)]

so. x-2 =13 => x=15
Senior Manager
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Now this becomes solvable...

2^x(1-2^-2) = 2^x * 3/4 = 3*2^(x-2) => x-2 = 13 => x=11
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chiragr wrote:
Now this becomes solvable...

2^x(1-2^-2) = 2^x * 3/4 = 3*2^(x-2) => x-2 = 13 => x=11

where did the 3/4 on the left side and 3 on the right side gone?
And in this kind of question it is easier to take out of parentheses the smallest exp try it
and X-2=13--->X=15
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Senior Manager
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I would strongly suggest every body to use () the right way ..
so that we can understand questions better.
SVP
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I got 15, and then on the second thought found the ambiguity.
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chiragr wrote:
Now this becomes solvable...

2^x(1-2^-2) = 2^x * 3/4 = 3*2^(x-2) => x-2 = 13 => x=11

Boy these mistakes will kill me on the first question it self...
x-2 =13 =>x=11? what was I thinking!
Director
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chiragr wrote:
chiragr wrote:
Now this becomes solvable...

2^x(1-2^-2) = 2^x * 3/4 = 3*2^(x-2) => x-2 = 13 => x=11

Boy these mistakes will kill me on the first question it self...
x-2 =13 =>x=11? what was I thinking!

Good that you on this forum)))
we all here to learn not to do this kind of mistakes!
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Director
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D without taking into consideration any paranthesis.
VP
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vbang do you copy us
Please come back and correct this convoluted question and give breather to guys here
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VP
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15 after assuming the paranthesis. Otherwise, no answer.
Manager
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x = 15
Yurik79's approach
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# If 2^x-2^{(x-2)} = 3*2^{13} , what is the value of x

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