Write the expression as a single natural logarithm 3 ln a - 1/2(ln b + ln c^2) can you show me how you got it ?

Rules
1)ln a+ln b=ln(a+b)
2) x ln(a)= ln(a)^x
3) ln(a) -jn(b) =ln (a/b)

so,
1) ln b + ln c^2 =ln(b/c²)
so,     3 ln a - 1/2(ln b + ln c^2)=3 ln a - 1/2ln(b/c²) = 3 ln a - ln(b/c²)^1/2 =

3 ln a - ln(b/c²)^1/2 =ln a³  - ln(b/c²)^1/2 = ln a³ - ln ((b^(1/2)/(c²)^(1/2))=
=  ln a³ - ln ((b^(1/2))/c) = ln ( a³ /((b^(1/2))/c) )= ln ( (a³ c)/(b^(1/2))

The answer is