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

If $\log 3 = 0.477$ and $(1000)^{x} = 3$,then $x$ equals

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:

If $\frac{\log x}{b-c} = \frac{\log y}{c-a} = \frac{\log z}{a-b}$,then $xyz = x^a \cdot y^b \cdot z^c = x^{b+c} \cdot y^{c+a} \cdot z^{a+b} = $

If $x=\log _{a} b c, y=\log _{b} c a, z=\log _{c} a b,$ then

If $\log (x-y) - \log 5 - \frac{1}{2} \log x - \frac{1}{2} \log y = 0$,then find the value of $\frac{x}{y} + \frac{y}{x}$.