Evaluate:

${\log }_5 125$

Evaluate:

${\log }_{16} 8$

Evaluate:

${\log }_{0.5} 16$

If ${\log }_{a}m=n$, express $a^{n-1}$ in terms of $a$ and $m$

Given ${\log }_{2}x=m$ and ${\log }_{5 }y=n$.

Express $2^{m-3}$ in terms of $x.$

Given ${\log }_{2}x=m$ and ${\log }_{5 }y=n$.

Express $5^{3n+2}$ in terms of $y.$

If ${\log }_{2}x=a$ and ${\log }_{3}y=a,$write ${72}^a$ in terms of $x$ and $y$.

Solve for $x : \log (x-1) + \log (x+1) = {\log }_{2}1$

If $\log (x^2- 21)=2$, show that $x=\pm 11$