What is u^2+2u-4ln(u)+2ln(y) ?

The solution to u^2+2u-4ln(u)+2ln(y) is u^2+2u+ln((y^2)/(u^4))

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simplify u^2+2u-4ln(u)+2ln(y)

simplify

u^{2} + 2 u - 4 ln (u) + 2 ln (y)

u^{2} + 2 u + ln (\frac{y ^{2}}{u ^{4}})

Solution steps

u^{2} + 2 u - 4 ln (u) + 2 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (u) = ln (u^{4})

= u^{2} + 2 u - ln (u^{4}) + 2 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= u^{2} + 2 u - ln (u^{4}) + ln (y^{2})

Apply log rule:

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

ln (y^{2}) - ln (u^{4}) = ln (\frac{y ^{2}}{u ^{4}})

= u^{2} + 2 u + ln (\frac{y ^{2}}{u ^{4}})

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

ln (x + 1) + ln (k)

ln (\frac{x}{e ^{x}})

ln (X) + ln (Y) - 3 ln (Z)

ln (a \cdot e^{- \frac{b}{x}})

What is u^2+2u-4ln(u)+2ln(y) ?
The solution to u^2+2u-4ln(u)+2ln(y) is u^2+2u+ln((y^2)/(u^4))