Question

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

Answer 1

Answer:

We conclude that:

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

Step-by-step 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:

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