If $\log _{10} 50+\log _{10} 20=x,$ then $x$ is equal to

$2 \log _{10} 5 + \log _{10} 8 - \frac{1}{2} \log _{10} 4 = ?$

If $0 < a < 1$,$0 < x < 1$,and $x < a$,then $\log_{a} x$ is:

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:

$\frac{\log _{9} 11}{\log _{5} 13}-\frac{\log _{3} 11}{\log _{\sqrt{5}} 13}=$

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