What is ln((1+t^2-2t)/(1+t^2+2t)) ?

The solution to ln((1+t^2-2t)/(1+t^2+2t)) is ln(1+t^2-2t)-ln(1+t^2+2t)

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simplify ln((1+t^2-2t)/(1+t^2+2t))

simplify

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

ln (1 + t^{2} - 2 t) - ln (1 + t^{2} + 2 t)

Solution steps

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

Apply log rule:

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

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

= ln (t^{2} - 2 t + 1) - ln (t^{2} + 2 t + 1)

ln (\frac{100}{150})

lo g_{2} (x) - lo g_{2} (x^{8})

- (\frac{1}{3} lo g_{e} (\frac{1}{3}) + \frac{2}{3} lo g_{e} (\frac{2}{3}))

ln (5 (10)) + e^{- 1.31 (10)}

\frac{1}{7} ln (x - 4) - \frac{1}{7} ln (x + 9)

What is ln((1+t^2-2t)/(1+t^2+2t)) ?
The solution to ln((1+t^2-2t)/(1+t^2+2t)) is ln(1+t^2-2t)-ln(1+t^2+2t)