Please need help on this one really need help on it

Step-by-step explanation:

Law of logarithm

LogAB = logA+logB

LogA/B= LogA -LogB

Also LogA^n= nLogA

So, we are going to use these three rules

Given that,

1. In(mn³/p)

Apply the division rule

Then,

In(mn³/p)= In(mn³) - In(p)

Also apply multiplication rule

In(mn³) - In(p) = In(m) + In(n³) - In(p)

Also apply the index rule

In(m) + In(n³) - In(p)

In(m) + 3In(n) - In(p)

Answer, the first option is the correct option

2. 3In(x)+2In(y)+loge(z)

Firstly loge is called natural logarithm which is also the In. Loge means In

Then, the question becomes

3In(x)+2In(y)+In(z)

Apply the rules above

First apply index rule

In(x³)+In(y²)+In(z)

Then, applying the addition rule

In(x³y²z). Answer

The second option is the correct answer