What is ln((\sqrt[4]{rs})/(u^2v)) ?

The solution to ln((\sqrt[4]{rs})/(u^2v)) is ln(\sqrt[4]{rs})-2ln(u)-ln(v)

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simplify ln((\sqrt[4]{rs})/(u^2v))

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^{2} v) = ln (u^{2}) + ln (v)

Apply log rule:

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

ln (u^{2}) = 2 ln (u)

- (2 ln (u) + ln (v)) : - 2 ln (u) - ln (v)

\frac{1}{2} (lo g_{9} (x) + lo g_{9} (y))

ln (\frac{e ^{7}}{8})

lo g_{10} (x^{2}) y

lo g_{3} (\frac{81}{x - 1})

lo g_{4} (\frac{a ( x + 3 ) ^{3}}{a - b ^{3}})

What is ln((\sqrt[4]{rs})/(u^2v)) ?
The solution to ln((\sqrt[4]{rs})/(u^2v)) is ln(\sqrt[4]{rs})-2ln(u)-ln(v)