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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.

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timetrader on 18 Jun 2009, 16:04, edited 1 time in total.

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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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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.

which one is your question?

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)

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ambiguish question

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Ambiguous question. Could be interpreted inmany ways without parentheses.

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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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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

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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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I would strongly suggest every body to use () the right way ..
so that we can understand questions better.

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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!

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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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D without taking into consideration any paranthesis.

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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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15 after assuming the paranthesis. Otherwise, no answer.

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x = 15
Yurik79's approach

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