Solve the equation forx.

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- Sep 24th 2009, 04:09 PM #1

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- Sep 2009
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- Sep 24th 2009, 04:25 PM #2

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- May 2009
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- 471

First note that 256=4^4 so we change the question into

$\displaystyle 4^{x-x^2}=\frac{1}{(4^4)^x}=\frac{1}{4^{4x}}$

Multiply both sides by $\displaystyle 4^{4x}$ to get $\displaystyle 4^{4x}\cdot 4^{x-x^2}=1$

$\displaystyle 4^{4x+x-x^2}=1$

$\displaystyle 4^{5x-x^2}=1$

And we need the exponent to be 0 since $\displaystyle x^0=1$ (you can take the log of both sides, but log 1=0 so we reach the same conclusion)

So now just solve $\displaystyle 5x-x^2=0$