What is ln(3v+w)-ln(w)+2-ln(v) ?

The solution to ln(3v+w)-ln(w)+2-ln(v) is ln((3v+w)/(vw))+2

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simplify ln(3v+w)-ln(w)+2-ln(v)

simplify

ln (3 v + w) - ln (w) + 2 - ln (v)

ln (\frac{3 v + w}{v w}) + 2

Solution steps

ln (3 v + w) - ln (w) + 2 - ln (v)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (3 v + w) - ln (w) = ln (\frac{3 v + w}{w})

= ln (\frac{3 v + w}{w}) + 2 - ln (v)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (\frac{3 v + w}{w}) - ln (v) = ln (\frac{\frac{3 v + w}{w}}{v})

= ln (\frac{\frac{3 v + w}{w}}{v}) + 2

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{3 v + w}{v w}) + 2

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What is ln(3v+w)-ln(w)+2-ln(v) ?
The solution to ln(3v+w)-ln(w)+2-ln(v) is ln((3v+w)/(vw))+2