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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{e} (\frac{3}{4} ln x^{2} + 2 + \frac{1}{2} ln ∣ x ∣)

ln (\frac{6}{5}) - ln (\frac{4}{6})

3 ln (\frac{5}{2}) + \frac{9}{10}

- \frac{1}{5} ln (x) - 5 [ln (y) - 3 ln (z)]

\frac{30 ln ( \frac{25}{114} )}{ln ( \frac{79}{114} )}

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