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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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