Answer:
We conclude that:
[tex]3\ln \left(m\right)+4\ln \left(n\right)=\ln \left(m^3n^4\right)[/tex]
Step-by-step explanation:
Given the expression
[tex]3\ln \left(m\right)+4\ln \left(n\right)[/tex]
Apply log rule:
- [tex]a\log _c\left(b\right)=\log _c\left(b^a\right)[/tex]
So the expression becomes
[tex]3ln\:m\:+\:4ln\:n=\ln \:\left(m^3\right)+\ln \:\left(n^4\right)[/tex]
Apply log rule:
[tex]\log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)[/tex]
so the expression becomes
[tex]=\ln \left(m^3n^4\right)[/tex]
Therefore, we conclude that:
[tex]3\ln \left(m\right)+4\ln \left(n\right)=\ln \left(m^3n^4\right)[/tex]
