What is ln((\sqrt[5]{rs})/(uv^3)) ?

The solution to ln((\sqrt[5]{rs})/(uv^3)) is ln(\sqrt[5]{rs})-ln(u)-3ln(v)

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simplify ln((\sqrt[5]{rs})/(uv^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 (u v^{3}) = ln (u) + ln (v^{3})

Apply log rule:

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

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

- (ln (u) + 3 ln (v)) : - ln (u) - 3 ln (v)

lo g_{b} (125 k)

lo g_{7} (\frac{x ^{3}}{x - 5})

- lo g_{10} (5 \cdot 1 0^{- 7})

2 lo g_{4} (5) + 2 lo g_{4} (11) + lo g_{4} (6)

ln (\frac{6}{e})

What is ln((\sqrt[5]{rs})/(uv^3)) ?
The solution to ln((\sqrt[5]{rs})/(uv^3)) is ln(\sqrt[5]{rs})-ln(u)-3ln(v)