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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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New post 27 Jul 2017, 07:12
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61% (01:36) correct 39% (01:53) wrong based on 581 sessions

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

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New post 27 Jul 2017, 07:35
3
2
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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Re: If x^2 = 2^x, what is the value of x ?  [#permalink]

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

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New post 07 Aug 2017, 05:45
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, 11:59
My 2 cents:
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If x^2 = 2^x, what is the value of x ?  [#permalink]

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New post 06 May 2018, 12:35
hey,
Still confused on statement 2
x=2^x-2
plugged that into x^2=2^x
2^(2x)-2^(2)=(2^x-2^2)
2x-2=2x-2
where I'm going wrong
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Re: If x^2 = 2^x, what is the value of x ?  [#permalink]

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New post 06 May 2018, 23:21
3
1
cocojatti92 wrote:
If \(x^2 = 2^x\), what is the value of x ?

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

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

hey,
Still confused on statement 2
x=2^x-2
plugged that into x^2=2^x
2^(2x)-2^(2)=(2^x-2^2)
2x-2=2x-2
where I'm going wrong


First of all, notice that (2) is \(x = 2^{x-2}\) (2 in power of x-2) not \(x = 2^x-2\).

\(x = 2^{x-2}\);

\(x = \frac{2^x}{4}\);

Since \(x^2 = 2^x\), then \(x = \frac{x^2}{4}\);

\(x(\frac{x}{4}-1)=0\);

x = 0 or x = 4.

Only x = 4 satisfies \(x^2 = 2^x\), this x = 4. Sufficient.

Hope it's clear.
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Re: If x^2 = 2^x, what is the value of x ?  [#permalink]

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New post 27 Sep 2018, 09:29
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What is the level of this question?
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Re: If x^2 = 2^x, what is the value of x ?  [#permalink]

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New post 17 Oct 2018, 22:21
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 Q



That 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!!
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Re: If x^2 = 2^x, what is the value of x ? &nbs [#permalink] 17 Oct 2018, 22:21
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