If $x = \log \left( y + \sqrt{y^2 + 1} \right)$, then $y =$

Evaluate: $\log _7(\log _7\sqrt {7\sqrt {7\sqrt 7 } }) = $

If ${\log _{10}}x = y$,then ${\log _{1000}}{x^2}$ is equal to

The sum of all the real solutions of the equation $ \log_{(x+3)}(6x^{2}+28x+30)=5-2\log_{(6x+10)}(x^{2}+6x+9) $ is equal to:

If $x, y, z$ are the sides of a right-angled triangle, where $z$ is the hypotenuse (largest side), then find the value of $\frac{1}{\log_{x+z} y} + \frac{1}{\log_{z-x} y}$.

The solution to the equation ${9^x} - {2^{x + 1/2}} = {2^{x + 3/2}} - {3^{2x - 1}}$ is: