What is ln((2x^2y)/(x^4+y^2)) ?

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

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simplify ln((2x^2y)/(x^4+y^2))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

lo g_{10} (32) + lo g_{10} (\frac{1}{8})

5 lo g_{10} (2) + 4 lo g_{10} (x)

5 lo g_{b} (x) - 3 lo g_{b} (y)

\frac{4 ln ( 2 )}{4 ln ( 5 ) - 5 ln ( 2 )}

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