Question

Let u= ln x and v=ln y. Write ln(x^3y^2) in terms of u and v.

Answer 1

A edge

Explanation:

Answer 2

a. 3u + 2v

Explanation:

To solve this problem, we need to apply some properties of logarithms. Properties are useful to simplify complicated expressions. Here we need to use a very useful property of logarithms called the logarithm of a product is the sum of the logarithms, that is:

`log_(b)(MN)=log_(b)(M)+log_(b)(N)`

From the function, it is then true that:

`ln(x^(3)y^(2))=ln(x^(3))+ln(y^(2))`

The other property we must use is Logarithm of a Power:

`log_(b)M^(n)=nlog_(b)M`

Then:

`ln(x^(3)y^(2))=ln(x^(3))+ln(y^(2)) \\ \\ ln(x^(3)y^(2))=3ln(x)+2ln(y)`

Since:

`u=ln(x) \\ v=ln(y)`

Then:

`ln(x^(3)y^(2))=3u+2v`

Finally, the correct option is:

a. 3u + 2v