Question

Write the expression as a single natural logarithm.

3 ln x - 2 ln c


A.

B. ln(x3 + c2)


C. ln(x3 - c2)


D. lnx3c2

Answer 1

3 In x - 2 In c = In x^3 - In c^2 = ln (x^3/c^2)

Answer 2

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

Explanation:

3 ln x - 2 ln c

We apply log properties

m log(a) = log a^m

We apply this property for each term

3 ln x becomes ln x^3 and 2ln c becomes ln c^2

`ln x^3 - ln c^2`

Now we apply one more property

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

`ln x^3 - ln c^2` becomes

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