Solve for $x$:

$\log x +\log 5 = 2 \log 3$

Solve for $x$:

$lo{g}_{3}x-lo{g}_{3}2=1$

Solve for $x:$

$x=\frac{\log 125}{\log 25}$

Solve for$x:$

$\frac{\log 8}{\log 2}\times \frac{\log 3}{\left(\log \sqrt{3}\right)}=2\log x$

Given $2{\log }_{10}x+1={\log }_{10}250$ , find $x$

If $2{\log }_{10}x+1={\log }_{10}250$, find ${\log }_{10}2x$.

Prove the following :

Prove the following :

${27}^{\log 2}=8^{\log 3}.$