What is ln(v^{-1/3})+ln((v-3)^{1/3})+c ?

The solution to ln(v^{-1/3})+ln((v-3)^{1/3})+c is ln(((v-3)/v)^{1/3})+c

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simplify ln(v^{-1/3})+ln((v-3)^{1/3})+c

simplify

ln (v^{- \frac{1}{3}}) + ln ((v - 3)^{\frac{1}{3}}) + c

ln ((\frac{v - 3}{v})^{\frac{1}{3}}) + c

Solution steps

ln (v^{- \frac{1}{3}}) + ln ((v - 3)^{\frac{1}{3}}) + c

Apply log rule:

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

ln (v^{- \frac{1}{3}}) + ln ((v - 3)^{\frac{1}{3}}) = ln (v^{- \frac{1}{3}} (v - 3)^{\frac{1}{3}})

= ln (v^{- \frac{1}{3}} (v - 3)^{\frac{1}{3}}) + c

Simplify

v^{- \frac{1}{3}} (v - 3)^{\frac{1}{3}} : (\frac{v - 3}{v})^{\frac{1}{3}}

= ln ((\frac{v - 3}{v})^{\frac{1}{3}}) + c

13 lo g_{10} (a) - lo g_{10} (b)

ln (\frac{x ^{2}}{x ^{2} + 1}) - \frac{1}{x} - arctan (x) + c

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What is ln(v^{-1/3})+ln((v-3)^{1/3})+c ?
The solution to ln(v^{-1/3})+ln((v-3)^{1/3})+c is ln(((v-3)/v)^{1/3})+c