$\displaystyle lgx^{4} - \frac{30}{lgx} = 2 $

I tried making lgx = y, but I can't get it to work.

Next problem is:

$\displaystyle log_{2}x - log_{4}x + log_{16}x = 3 $

I managed to get it down to $\displaystyle \frac{4}{4log_{x^{2}}} - \frac{2}{4log_{x^{2}}} + \frac{1}{4log_{x^{2}}} = 3 $

but I don't know what next. The end result should be 16.

And what about these two:

$\displaystyle \frac{z}{2 + lgx} + \frac{z}{4-lgx} = 1 $

and

$\displaystyle log_{x}3 + log_{3}x = 2 $

What I did, was $\displaystyle log_{x}3 + \frac{1}{log_{x}3} = 2 $

Then, $\displaystyle log_{x}3 = y $ and that's where I'm stuck. What I get is: $\displaystyle y+\frac{1}{y}=2 $ I can't get a squared y out of it. And I don't know how to deal with the fraction.

Please reply,

Thanks!