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

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by Anurag@Gurome » Thu Jan 06, 2011 9:08 am
Viper83 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
.... (2)^x - (2)^(x - 2) = 3(2^13)
=> (2)^(x - 2 + 2) - (2)^(x - 2) = 3(2^13) ............... Write x as (x + 2 - 2)
=> (2²)*[(2)^(x - 2)] - (2)^(x - 2) = 3(2^13) ........... Take 2² outside
=> 4*[(2)^(x - 2)] - (2)^(x - 2) = 3(2^13)
=> [(2)^(x - 2)]*(4 - 1) = 3(2^13) ........................... (2)^(x - 2) is common
=> 3*[(2)^(x - 2)] = 3(2^13)
=> (2)^(x - 2) = (2^13)
=> (x - 2) = 13 ........................................................... Equating the power of 2
=> x = 15

The correct answer is D.
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by captcha » Thu Jan 06, 2011 10:30 am
If (2^x)-(2^x-2)=3(2^13), what is the value of x?

let 2^x = a
so 2^(x-2)=2^x/2^2 = 2^x/4 = 0.25 * 2^x = 0.25a

=>a-.25a=3(2^13)
=>3/4a=3(2^13)
a=4*2^13 = 2^2*2^13 = 2^15

so 2^x=2^15

=>x=15
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by GMATGuruNY » Thu Jan 06, 2011 11:42 am
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
We can plug in the answer choices for x. The process will be just as fast as algebra and far less messy.

Answer choice C: x= 13
2^13 - 2^(13-2) = 3(2^13)
2^13 - 2^11 = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

Plugging in x=13 made the exponent on the left 2^11.
To match 2^13 on the right side of the equation, the exponent needs to be increased by 2.
Thus, x = 13+2 = 15.

The correct answer is D.
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