Answer:
[tex](A)ln 2+3lna-4ln b[/tex]
Step-by-step explanation:
Given the expression: [tex]ln \dfrac{2a^3}{b^4}[/tex]
We apply the following laws of logarithm to expand:
[tex]Log (ab)=Log a+Log b\\Log(a/b)=Log a-Log b\\Log a^x=xLog a[/tex]
Therefore:
[tex]ln \dfrac{2a^3}{b^4}=ln 2a^3-ln b^4\\=ln 2+lna^3-ln b^4\\=ln 2+3lna-4ln b[/tex]
