[tex]\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)
\\ \quad \\\\
% Logarithm of rationals
log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y)
\\ \quad \\\\
% Logarithm of exponentials
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\
-----------------------------\\\\
ln\left( \cfrac{6x^9}{y^5} \right)\implies ln(6x^9)-ln(y^5)\implies ln(6)+ln(x^9)-ln(y^5)
\\\\\\
ln(6)+9ln(x)-5ln(y)[/tex]
