# Math Help - problem: (log2(x^2))^2 - log2(2x) = 2

1. ## problem: (log2(x^2))^2 - log2(2x) = 2

Hi.

I have a problem with a task:

(log2(x^2))^2 - log2(2x) = 2, solve for x.

i dont see this working out to become a quadratic equation in any way and getting the left part on the log2 base so i could use the loga - logb = log a/b got me as far as log2 (x^2logx)/2x = 2, so I'm stuck.
Please help.

Thank you.

2. ## Re: problem: (log2(x^2))^2 - log2(2x) = 2

Originally Posted by mathpersson
Hi.

I have a problem with a task:

(log2(x^2))^2 - log2(2x) = 2, solve for x.

i dont see this working out to become a quadratic equation in any way and getting the left part on the log2 base so i could use the loga - logb = log a/b got me as far as log2 (x^2logx)/2x = 2, so I'm stuck.
Please help.

Thank you.
\displaystyle \begin{align*} \left[\log_2{\left(x^2\right)} \right]^2 - \log_2{\left(2x\right)} &= 2 \\ \left[2\log_2{(x)}\right]^2 - \left[ \log_2{(2)} + \log_2{(x)} \right] &= 2 \\ 4\left[\log_2{(x)}\right]^2 - 1 - \log_2{(x)} &= 2 \\ 4\left[\log_2{(x)}\right]^2 - \log_2{(x)} - 3 &= 0 \end{align*}

Now solve the resulting quadratic...

3. ## Re: problem: (log2(x^2))^2 - log2(2x) = 2

thank you so much