Question

Expand: In 2a^3/b^4

In 2 + 3 In a - 4 In b

In 2 - 3 In a - 4 In b

In 2 - 3 In a + 4 In b

Answer 1

`(A)ln 2+3lna-4ln b`

Explanation:

Given the expression:
`ln (2a^3)/(b^4)`

We apply the following laws of logarithm to expand:

`Log (ab)=Log a+Log b\\Log(a/b)=Log a-Log b\\Log a^x=xLog a`

Therefore:

`ln (2a^3)/(b^4)=ln 2a^3-ln b^4\\=ln 2+lna^3-ln b^4\\=ln 2+3lna-4ln b`