Question

Let u=ln x and v= ln y. Write ln y^7/x^5 in terms of u and v

Answer 1

7v-5u

Explanation:

ln(y⁷/x⁵)

ln(y⁷) - ln(x⁵)

7lny - 5lnx

7v - 5u

Answer 2

7v - 5u

Explanation:

Our expression is:
`ln((y^7)/(x^5) )`. Remember the property of ln, where ln(a / b) = ln(a) - ln(b). We can apply that here:

`ln((y^7)/(x^5) )` = ln(
`y^7`) - ln(
`x^5`)

Now, also remember that when we have ln(
`a^b`), we can write it as b * ln(a). Apply this here:

ln(
`y^7`) = 7ln(y)

ln(
`x^5`) = 5ln(x)

Notice that since u = ln(x) and v = ln(y), we can replace those respectively:

7ln(y) = 7v

5ln(x) = 5u

Put it together:

`ln((y^7)/(x^5) )` = 7v - 5u