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

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

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

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

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

Apply log rule:

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

2 ln (uv) = 2 ln (u) + 2 ln (v)

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

ln (2) 2

2 lo g_{a} (w) - \frac{1}{2} lo g_{a} (z) + 4 lo g_{a} (y)

ln (\frac{s ^{2} + 49}{s ^{2} + 25})

ln (y \frac{y}{7 - y})

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

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