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