exponential equation.

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jagdish
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exponential equation.

Unread post by jagdish » Sun Jan 22, 2012 7:59 pm

no. of real solution of the equation $4^x = x^2$
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zadid xcalibured
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Re: exponential equation.

Unread post by zadid xcalibured » Thu Feb 28, 2013 3:02 am

The given equation splits up into $2$ different equations.
$2^x=x$ for positive $x$. and $2^x=-x$ for negative $x$.
That means the equation we have to solve is this $2^x=|x|$
When $x$ is negative the left side is less than $1$ and tending to $0$.So no solution in this case.
If $x$ is positive the graph is a convex function starting from $0$.where the line $y=x$ is below the graph.So they never intersect.

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*Mahi*
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Re: exponential equation.

Unread post by *Mahi* » Thu Feb 28, 2013 9:42 am

zadid xcalibured wrote: When $x$ is negative the left side is less than $1$ and tending to $0$.So no solution in this case.
This statement is not quite right, there is one intersection, as RHS goes from $0$ to $\infty$ and LHS goes from $1$ to $0$ for $x= 0 \text{ to } -\infty $, and as both are strictly increasing/decreasing functions.
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zadid xcalibured
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Re: exponential equation.

Unread post by zadid xcalibured » Thu Feb 28, 2013 1:48 pm

How could i do this kind of shitty thing?????????? :mrgreen: I don't know who gave me the right to turn a curve into a straight line. :mrgreen: The first mistake is where i eliminated the square. :mrgreen: But the problem is pretty easy. :mrgreen:

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*Mahi*
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Re: exponential equation.

Unread post by *Mahi* » Thu Feb 28, 2013 2:59 pm

zadid xcalibured wrote:I don't know who gave me the right to turn a curve into a straight line. :mrgreen: The first mistake is where i eliminated the square. :mrgreen:
I don't think that was a mistake, actually, it was a nice idea to eliminate the square.
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