Question

Simplify/Condense the attached problem. Thanks!

Answer 1

ok log properties


`log_ax+log_ay=log_a(xy)`
and

`(log_ax)/(log_ay) log_a(x-y)`
and

`nlog_ax=log_ax^n`

so

pemdas
first make like fractions so we can combine

`(2log_bx)/(3) + (3log_by)/(4)`
times first fraction by 4/4 and second by 3/3

`(8log_bx)/(12) + (9log_by)/(12)`
combine fractions

`(8log_bx+9log_by)/(12)`
now move fractions up

`(log_b(x^8y^9))/(12)`

now the other part

`(log_b(x^8y^9))/(12)-5log_bz`
we need to combine that
`5log_bz` with that
`(log_b(x^8y^9))/(12)` by make it als a fraction of common denomenator of 12
multiply
`5log_bz` by 12/12

`(60log_bz)/(12)`
move the coefient to expoment

`(log_bz^(60))/(12)`

now conbine fractions


`(log_b(x^8y^9))/(12) - (log_b(z^(60)))/(12)`

`(log_b(x^8y^9)-log_b(z^(60)))/(12)}{12}`
apply log property

`(log_b (x^8y^9)/(z^(60)) )/(12)`