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

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

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

simplify

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

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

Solution steps

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

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}})

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}})

ln (\frac{c}{x y}) - e^{x y}

ln (A^{x} B^{y})

ln (x^{y} \cdot (1 - x)^{z - y})

0.0259 \cdot ln (\frac{4.7 \cdot 1 0 ^{17}}{1.15 \cdot 1 0 ^{14}})

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