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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

\frac{1}{2} lo g_{5} (2)

ln (\frac{x}{400})

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

\frac{3}{6} \cdot ln (\frac{z - 3}{z + 3}) - \frac{1}{2} \cdot ln (z^{2} - 9)

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

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