Question

Write ln2x+2lnx-ln3y as a single logarithm.

a. ln(2x/3y)

b. ln(3x/3y)

c. ln(2x^3/3y)

d. ln(x^3/3y)

Answer is C. ln(2x^3/3y) on Edge!

Answer 1

Option C.
`ln((2x^(3))/(3y))`

Explanation:

The given logarithmic expression is:

`ln(2x)+2ln(x)-ln(3y)`

Using the power rule of logarithms:
`blog(a)=log(b)^(a)`, the above expression can be written as:

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

Using the product rule of logarithms:
`log(a)+log(b) =log(ab)`, the above expression can be simplified further to:

`ln(2x * x^(2)) - ln(3y)\\\\=ln(2x^(3))- ln(3y)`

Using the quotient rule of logarithms:
`log(a)-log(b)=log((a)/(b))`, the above expression can be written as:

`ln((2x^(3))/(3y))`

Hence option C gives the correct simplified answer.