What is ln((\sqrt[7]{mn})/(pq^3)) ?

The solution to ln((\sqrt[7]{mn})/(pq^3)) is ln(\sqrt[7]{mn})-ln(p)-3ln(q)

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simplify ln((\sqrt[7]{mn})/(pq^3))

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

ln (p q^{3}) = ln (p) + ln (q^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (q^{3}) = 3 ln (q)

- (ln (p) + 3 ln (q)) : - ln (p) - 3 ln (q)

ln (x) - ln (5 x)

ln (\frac{θ ^{2} ( 3 - 2 θ )}{36})

ln (6 y)

6 lo g_{5} (x) - 36 lo g_{5} (y)

lo g_{4} (\frac{\frac{x}{z}}{w})

What is ln((\sqrt[7]{mn})/(pq^3)) ?
The solution to ln((\sqrt[7]{mn})/(pq^3)) is ln(\sqrt[7]{mn})-ln(p)-3ln(q)