Answer :
Answer:
Option C. [tex]ln(\frac{2x^{3}}{3y})[/tex]
Step-by-step explanation:
The given logarithmic expression is:
[tex]ln(2x)+2ln(x)-ln(3y)[/tex]
Using the power rule of logarithms: [tex]blog(a)=log(b)^{a}[/tex], the above expression can be written as:
[tex]ln(2x)+ln(x)^{2}-ln(3y)[/tex]
Using the product rule of logarithms: [tex]log(a)+log(b) =log(ab)[/tex], the above expression can be simplified further to:
[tex]ln(2x \times x^{2}) - ln(3y)\\\\=ln(2x^{3})- ln(3y)[/tex]
Using the quotient rule of logarithms: [tex]log(a)-log(b)=log(\frac{a}{b})[/tex], the above expression can be written as:
[tex]ln(\frac{2x^{3}}{3y})[/tex]
Hence option C gives the correct simplified answer.