# Thread: logs

1. ## logs

Let x be a positive real number not equal to 1. Determine the region of the x-1 plane containing the solutions to the inequality :

Logx(Logx(y^2))>0

Show your answer as a shaded region.

Thank you very much! I appreaciate your help!

2. Which of these is your problem?
$\displaystyle \log \left[ x \right]\log \left[ {x\left( {y^2 } \right)} \right] > 0\,or\,\log _x \left[ {\log _x \left( {y^2 } \right)} \right] > 0$

Or is it something else?

3. It's the second one Plato. Thank you very much!

4. $\displaystyle \begin{array}{l} \log _x (a) > 0\quad \Rightarrow \quad a > 1 \\ \log _x \left( {\log _x \left( {y^2 } \right)} \right) > 0\quad \Rightarrow \quad \log _x \left( {y^2 } \right) > 1\quad \Rightarrow \quad y^2 > x > 0 \\ \end{array}$