Question

Write as a single logarithm

Answer 1

`c. \ln( \frac{2 {x}^(3) }{3y})`

Step-by-step explanation

We want to write

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

as a single logarithm.

Use the power rule to rewrite the middle term:

`n \: ln(a) = ln( {a}^(n) )`

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

Use the product rule to obtain:

`ln(a) + ln(b) = ln(ab)`

`ln(2x * {x}^(2) )- ln(3y)`

`ln(2{x}^(3) )- ln(3y)`

Apply the quotient rule:

`ln(a) - ln(b) = ln( (a)/(b))`

`ln(2{x}^(3) )- ln(3y) =\ln(\frac{2 {x}^(3) }{3y})`