chetan2u wrote:

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 QThat was a very helpful solution!!

Chetan,

I have a query. I was able to solve the eqautions and get the values but I didnt plug in back and check that in the main equation.So I chose E

Can you please explain when and what pattern do you see and keep a check a to plugin back the multiple values.

For example in modules questions we do...do you also check for plolynomial degree equations..

Please tell your line of thinking/approach when attempting this variety of questions!!