2ln(x-3)-ln6-3ln(x+2)

2lnx-3-ln6-3lnx2

#1

2ln(x-3)-ln6-3ln(x+2)

Answer:

Make the coefficients of ln terms 1 using power property, and then apply product property.
The final answer is ln{(x-3)^2/6*(x+2)^3}

we know that,
Property I --> a.ln(b) = ln(b^a)
Property II --> ln(x) - ln(y) = ln(x/y)
using these properties, we get
2ln(x-3) = ln(x-3)^2
3ln(x+2) = ln(x+2)^3
hence
2ln(x-3) - 3ln(x+2) - ln6 = ln(x-3)^2 - ln(x+2)^3 - ln6 ( Using Property I)
further
ln(x-3)^2 - ln(x+2)^3 - ln6 = ln [{(x-3)^2/(x+2)^3}/6] (Using Property II)