Find the smallest real number x, correct to the nearest hundredth, which satisfies the equation:

(log(sub 2) x)^3 - log(sub 2)(2x^3)=(log(sub 2))^2-log(sub 2)(x^2) - log(sub 2)(2)

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- Feb 3rd 2008, 12:39 PM #1

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- Feb 3rd 2008, 12:59 PM #2

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- Feb 3rd 2008, 01:26 PM #3

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- Feb 3rd 2008, 01:32 PM #4
you tell us, does it look like what your text says it should look like?

anyway, simplify the logarithms first.

you have: $\displaystyle (\log_2 x)^3 - \log_2 2 - 3 \log_2 x = (\log_2 x)^2 - 2 \log_2 x - 1$ ............(any questions about changing the logarithms?)

now let $\displaystyle \log_2 x$ be $\displaystyle y$, so you really want to solve:

$\displaystyle y^3 - 1 - 3y = y^2 - 2y - 1$

can you solve that?

when done, just replace $\displaystyle y$ with $\displaystyle \log_2 x$ and solve for $\displaystyle x$