[tex]\bf \textit{Logarithm of rationals}\\\\
log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y)
\\\\\\
\textit{Logarithm Cancellation Rules}\\\\
log_{{ a}}{{ a}}^x\implies x\qquad \qquad
{{ a}}^{log_{{ a}}x}=x\\\\
-------------------------------\\\\[/tex]
[tex]\bf log_3(4)-log_3(x)=2\implies log_3\left( \frac{4}{x} \right)=2\impliedby
\begin{array}{llll}
now\ we\\
exponentialize\\
both\ sides
\end{array}
\\\\\\
3^{log_3\left( \frac{4}{x} \right)}=3^2\implies \cfrac{4}{x}=3^2\implies \cfrac{4}{9}=x[/tex]
