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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

(\frac{1}{( 1.21 \cdot 1 0 ^{(- 4)} )}) \cdot ln (\frac{15.3}{5.22})

0.199 ln (\frac{0.105}{0.075})

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

\frac{1}{20} ln (\frac{33}{28})

lo g_{2} (ab)

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