What is ln((3v+w)/(vw))+2 ?

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

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simplify ln((3v+w)/(vw))+2

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (v w) = ln (v) + ln (w)

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

- (ln (v) + ln (w)) : - ln (v) - ln (w)

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

2 \cdot ln (1 + y) - ln (1 + x)

- 2 ln (5) + 2 ln (2)

ln (3 y^{2})

lo g_{10} (a) - 2 lo g_{10} (b) + 3

ln (16) + ln (7) - 3 ln (2)

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