If $\log _{x} y=100$ and $\log _{2} x=10,$ then the value of $y$ is

For $x>0,$ if $y=\frac{10^{\log _{10} x}}{x^{2}}$ and $x=y^{a},$ then $a=$

$\frac{\log \sqrt{8}}{\log 8}$ is equal to

If $\log_{10} 2 = 0.3010$ and $\log_{10} 3 = 0.4771$,then the number of zeros between the decimal point and the first significant figure in $(0.0432)^{10}$ is:

$\log _{10} \tan 40^{\circ} \cdot \log _{10} \tan 41^{\circ} \cdots \log _{10} \tan 50^{\circ} = ?$

If $\frac{\log x}{l+m-2n} = \frac{\log y}{m+n-2l} = \frac{\log z}{n+l-2m}$,find the value of $x^2 y^2 z^2$.