What is ((-x)/(x+y))+(ln(x^2+y^2)-2ln(x)) ?

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

Popular >

simplify ((-x)/(x+y))+(ln(x^2+y^2)-2ln(x))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- lo g_{10} (4.21 \cdot 1 0^{- 5})

- lo g_{10} (3.7 \cdot 1 0^{- 7})

ln (\frac{210 e ^{x}}{4.1 + 1.2 e ^{x}})

ln (\frac{21}{2 x}) - ln_{4} (21)

\frac{1}{6} ln (\frac{x - 3}{x + 3})

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