ok log properties
\(log_ax+log_ay=log_a(xy)\)
and
\(\frac{log_ax}{log_ay} log_a(x-y)\)
and
\(nlog_ax=log_ax^n\)
so
pemdas
first make like fractions so we can combine
\(\frac{2log_bx}{3} + \frac{3log_by}{4}\)
times first fraction by 4/4 and second by 3/3
\(\frac{8log_bx}{12} + \frac{9log_by}{12}\)
combine fractions
\(\frac{8log_bx+9log_by}{12}\)
now move fractions up
\(\frac{log_b(x^8y^9)}{12}\)
now the other part
\(\frac{log_b(x^8y^9)}{12}-5log_bz\)
we need to combine that \(5log_bz\) with that \(\frac{log_b(x^8y^9)}{12}\) by make it als a fraction of common denomenator of 12
multiply \(5log_bz\) by 12/12
\(\frac{60log_bz}{12}\)
move the coefient to expoment
\(\frac{log_bz^{60}}{12}\)
now conbine fractions
\(\frac{log_b(x^8y^9)}{12} - \frac{log_b(z^{60})}{12}\)
\(\frac{log_b(x^8y^9)-log_b(z^{60})}{12}}{12}\)
apply log property
\(\frac{log_b \frac{x^8y^9}{z^{60}} }{12}\)
