The product of the roots of the equation $$\log_{2}2^{(\log_{2}x)^{2} }− 5\log_{2}x + 6 = 0$$ is ________

We know that log_nn^x = x

Using the same property on  $$\log_{2}2^{(\log_{2}x)^{2} }$$, we get $$\log_22^{(\log_2x)^2}=\left(\log_2x\right)^2$$

$$\log_{2}2^{(\log_{2}x)^{2} }− 5\log_{2}x + 6 = 0$$ can be re written as  $$(\log_{2}x)^{2} − 5\log_{2}x + 6 = 0$$

$$\log_2x=k$$

Replacing $$\log_2x$$ with k, will give us a quadratic equation in k. 

$$k^2-5k+6=0$$

The roots of this equation are k = 2 and 3

$$\log_2x=2$$ This gives us the value of x as 4

$$\log_2x=3$$ And the value of from this equation is x = 8

The product = 8*4 = 32