What is log_{3}(((x+4)^2)/(x^2+y^2)) ?

The solution to log_{3}(((x+4)^2)/(x^2+y^2)) is 2log_{3}(x+4)-log_{3}(x^2+y^2)

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simplify log_{3}(((x+4)^2)/(x^2+y^2))

simplify

lo g_{3} (\frac{( x + 4 ) ^{2}}{x ^{2} + y ^{2}})

2 lo g_{3} (x + 4) - lo g_{3} (x^{2} + y^{2})

Solution steps

lo g_{3} (\frac{( x + 4 ) ^{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 + 4 ) ^{2}}{x ^{2} + y ^{2}}) = lo g_{3} ((x + 4)^{2}) - lo g_{3} (x^{2} + y^{2})

= lo g_{3} ((x + 4)^{2}) - lo g_{3} (x^{2} + y^{2})

Simplify

lo g_{3} ((x + 4)^{2}) : 2 lo g_{3} (x + 4)

= 2 lo g_{3} (x + 4) - lo g_{3} (x^{2} + y^{2})

2 lo g_{6} (u) + 7 lo g_{6} (v)

lo g_{5} (\frac{x ^{4} y ^{9}}{z ^{6}})

\frac{1}{2} [lo g_{2} (x) + lo g_{2} (x + 1)]

ln (\frac{x ^{2} - x - 2}{( x + 4 ) ^{2}})^{\frac{1}{3}}

\frac{1}{2} ln 2 + 2 v^{2} - \frac{1}{2} arctan (v) + ln (x)

What is log_{3}(((x+4)^2)/(x^2+y^2)) ?
The solution to log_{3}(((x+4)^2)/(x^2+y^2)) is 2log_{3}(x+4)-log_{3}(x^2+y^2)