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If x^2 = 2^x, what is the value of x ?

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If x^2 = 2^x, what is the value of x ? [#permalink]

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59% (01:21) correct 41% (01:45) wrong based on 140 sessions

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Re: If x^2 = 2^x, what is the value of x ? [#permalink]

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carcass wrote:
If \(x^2 = 2^x\), what is the value of x ?


(1) \(2x = (\frac{x}{2})^3\)

(2) \(x = 2^x-2\)


Hi..

If \(x^2 = 2^x\), what is the value of x ?


(1) \(2x = (\frac{x}{2})^3\)
\(x*(\frac{x^2}{8}-2)=0\)
we get x as 0, 4 or -4..
when we substitute value in \(x^2 = 2^x\), ONLY x = 4 is possible..
sufficient


(2) \(x = 2^x-2\)
or \(x+2=2^x\)...
2^x has to be multiple of 2 and so also x+2 should be in power of 2 that is 2,4,8,16...AND x+2 will fit in only at x+2=4 as 2^2
ONLY when x is 2 both sides are 4.
.
suff

although ans is D, but values of x differ as 4 in statement I and 2 in II
generally not possible in OG..

carcass i believe statement II should be \(x=2^{x-2}\).. here possible value is 4 SAME as statement I.. pl relook into Q
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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New post 07 Aug 2017, 06:45
Statement II can be turned into 4x=2^x which clearly has the only answer x=4, so it is sufficient

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Re: If x^2 = 2^x, what is the value of x ? [#permalink]

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New post 12 Aug 2017, 12:59
My 2 cents:
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Re: If x^2 = 2^x, what is the value of x ?   [#permalink] 12 Aug 2017, 12:59
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