1. Log problem

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)

2. Please write this out using LaTeX i can't really read the questions properly

\log _{2}{x^n} around the math tags gives $\log _{2}{x^n}$

3. $(log _{2}{x})^3 - log_{2}({2x^3})=(log_{2}{x})^2 - log_{2}({x^2}) - log_{2}{2}$

Like that?

4. Originally Posted by LordHz
$(log _{2}{x})^3 - log_{2}({2x^3})=(log_{2}{x})^2 - log_{2}({x^2}) - log_{2}{2}$

Like that?
you tell us, does it look like what your text says it should look like?

anyway, simplify the logarithms first.

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

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

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

can you solve that?

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