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

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 $\frac{\log x}{a^{2}+a b+b^{2}}=\frac{\log y}{b^{2}+b c+c^{2}}=\frac{\log z}{c^{2}+c a+a^{2}}$,then $x^{a-b} \cdot y^{b-c} \cdot z^{c-a}=$

$\frac{3+\log _{10} 343}{2+\frac{1}{2} \log _{10} \left(\frac{49}{4}\right)+\frac{1}{3} \log _{10} \left(\frac{1}{125}\right)}=$

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

If $3^{x-2}=5$ and $\log_{10} 2=0.30103, \log_{10} 3=0.4771$,then $x=$