What is 2(ln(u^3)+ln(w^{1/3})-ln(v)) ?

The solution to 2(ln(u^3)+ln(w^{1/3})-ln(v)) is 2ln((u^3w^{1/3})/v)

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simplify 2(ln(u^3)+ln(w^{1/3})-ln(v))

simplify

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

2 ln (\frac{u ^{3} w ^{\frac{1}{3}}}{v})

Solution steps

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

Apply log rule:

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

ln (u^{3}) + ln (w^{\frac{1}{3}}) = ln (u^{3} w^{\frac{1}{3}})

= 2 (ln (u^{3} w^{\frac{1}{3}}) - ln (v))

Apply log rule:

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

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

= 2 ln (\frac{u ^{3} w ^{\frac{1}{3}}}{v})

lo g_{9} (x - 5) + lo g_{9} (x + 5)

ln^{2} (x) + 2 ln (x) + 2

ln (\frac{( 1 - x ^{4} ) ^{2}}{( 1 + x ^{4} ) ^{2}})

lo g_{10} (\frac{x}{10000 y ^{2}})

3 ln (3) - 4 ln (2)

What is 2(ln(u^3)+ln(w^{1/3})-ln(v)) ?
The solution to 2(ln(u^3)+ln(w^{1/3})-ln(v)) is 2ln((u^3w^{1/3})/v)