If $a^{x} = b^{y}$,then

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 $\log_{10} 2 = 0.3010$,then $\log_{10}(1/2) =$

$\log _{5}\left(1+\frac{1}{5}\right)+\log _{5}\left(1+\frac{1}{6}\right)+\log _{5}\left(1+\frac{1}{7}\right)+\cdots+\log _{5} \left(1+\frac{1}{624}\right)$

If $\frac{\log _{2} a}{2}=\frac{\log _{3} b}{3}=\frac{\log _{4} c}{4}$ and $a^{1 / 2} \cdot b^{1 / 3} \cdot c^{1 / 4}=24$,then:

If $\log \left(\frac{x+y}{5}\right) = \frac{1}{2}(\log x + \log y),$ then $\frac{x}{y} + \frac{y}{x} = $