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

Sagot :

absor201

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]

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