Question

Write the expression as a single natural logarithm.
3lnm+4lnn

Answer 1

We conclude that:

`3\ln \left(m\right)+4\ln \left(n\right)=\ln \left(m^3n^4\right)`

Explanation:

Given the expression

`3\ln \left(m\right)+4\ln \left(n\right)`

Apply log rule:

• 
  `a\log _c\left(b\right)=\log _c\left(b^a\right)`

So the expression becomes

`3ln\:m\:+\:4ln\:n=\ln \:\left(m^3\right)+\ln \:\left(n^4\right)`

Apply log rule:

`\log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)`

so the expression becomes

`=\ln \left(m^3n^4\right)`

Therefore, we conclude that:

`3\ln \left(m\right)+4\ln \left(n\right)=\ln \left(m^3n^4\right)`