What is log_{3}(((x+y)^2)/(x^2+y^2)) ?

The solution to log_{3}(((x+y)^2)/(x^2+y^2)) is 2log_{3}(x+y)-log_{3}(x^2+y^2)

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simplify log_{3}(((x+y)^2)/(x^2+y^2))

simplify

lo g_{3} (\frac{( x + y ) ^{2}}{x ^{2} + y ^{2}})

2 lo g_{3} (x + y) - lo g_{3} (x^{2} + y^{2})

Solution steps

lo g_{3} (\frac{( x + y ) ^{2}}{x ^{2} + y ^{2}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{( x + y ) ^{2}}{x ^{2} + y ^{2}}) = lo g_{3} ((x + y)^{2}) - lo g_{3} (x^{2} + y^{2})

= lo g_{3} ((x + y)^{2}) - lo g_{3} (x^{2} + y^{2})

Simplify

lo g_{3} ((x + y)^{2}) : 2 lo g_{3} (x + y)

= 2 lo g_{3} (x + y) - lo g_{3} (x^{2} + y^{2})

lo g_{4} (x^{2} - 49) - 6 lo g_{4} (x + 7)

lo g_{b} (x y^{3})

ln (\frac{1}{n})

lo g_{4} (x^{2} - 4) - 4 lo g_{4} (x + 2)

3 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

What is log_{3}(((x+y)^2)/(x^2+y^2)) ?
The solution to log_{3}(((x+y)^2)/(x^2+y^2)) is 2log_{3}(x+y)-log_{3}(x^2+y^2)