The product of all the solutions of the equation $x^{1 + \log_{10} x} = 100000x$ is

The equation $x^{(3/4)(\log_2 x)^2 + (\log_2 x) - 5/4} = \sqrt{2}$ has

If $\log_{0.3}(x - 1) < \log_{0.09}(x - 1)$,then $x \ne 1$ lies in

$\log (\cosh 3 + \sinh 3) + \log (\cosh 3 - \sinh 3) = $

Let $m$ be the minimum possible value of $\log _3(3^{y_1}+3^{y_2}+3^{y_3})$,where $y_1, y_2, y_3$ are real numbers for which $y_1+y_2+y_3=9$. Let $M$ be the maximum possible value of $(\log _3 x_1+\log _3 x_2+\log _3 x_3)$,where $x_1, x_2, x_3$ are positive real numbers for which $x_1+x_2+x_3=9$. Then the value of $\log _2(m^3)+\log _3(M^2)$ is:

If $a^2 + 4b^2 = 12ab$,then $\log(a + 2b) =$